Solve y(4xy)dx 2(x^2y)dy = 0 by finding the integrating factor and test for exactness Expert Answer Previous question Next question Get more help from Chegg Solve it with our calculus problem solver and calculatorAn ordinary differential equation of first order and first degree can be written as dy dx = f(x,y) d y d x = f ( x, y) , where f(x,y) f ( x, y) is a function of two variables x,y x, y Which canSolve dy/dx = x/y , y(0) = 3 Differential equations A differential equation is any equation which contains a function and one or more of it's derivatives The solution to a differential
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(x*y^2+x)dx+(y-x^2y)dy=0-The equation is M(x,y)dx N(x,y)dy =0 , with M = 4xy 3y^2 x , M_y = 4x 6y N = x(x 2y) , N_x = 2x 2y # M_y The equation is not exact but ( M_y N_x )/N = 2/x , depends only on x and leads to the integrating factor IF = x^2 One obtains the equation P(x,y)dx Q(x,y)dy =0 with P = 4yx^3 3y^2x^2 x^3 , P_y = 4x^3 6yx^2ANSWER IS Solution For a differential equation M(x,y) dx N(x,y) dy= 0 The necessary and sufficient condition for exact differential equation is ∂M/∂y = ∂N/∂x Here the equation is not exact if M(x,y) dx N(x,y) dy = 0 is of the from f(x,y)y dx g
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Solve the differential equation dy/dx = (2y^2cos x y sin2x 2cos xsin^2x)/sin^2x asked in Differential equations by Nakul01 ( 369k points) differential equationsFactor integrador = e ^ ∫ 1 / y dy = e ^ ln y = y Multiplicar por y y² (x y 1) dx xy (x 3y 2) dy = 0 (xy² y³ y²) dx (x²y 3xy² 2xy) dy = O La ecuación ahora es exacta La solución es F (x, y) = C, donde ∂F / ∂x = M (x, y) = (xy² y³ y²) F (x, y) = ∫ (xy² y³ y²) dx Explanation x dy dx = 2x2y y, separating the variables 1 y dy dx = 2x2 1 x so dy y = 2x2dx dx x, integrating ∫ 1 y dy = ∫2x2dx ∫ 1 x dx, we have lny = x2 lnx C Which gives ln y x = x2 C eln y x = ex2c theory of logs ie, y x = ex2c and so,y
But if I expand the bracket $(xy)^2$ before integrating I will get $$\varnothing_1=\int Mdx=\int (xy)^2dx=\int (x^22xyy^2)dx=\frac{x^3}{3}xy^2x^2y$$ Wich will lead to the solution $$\varnothing=\varnothing_1\varnothing_2=\frac{x^3}{3}xy^2x^2yy=Constant$$ What is the wrong step ? Show that the differential equation (x y) (dy)/dx = x 2y is homogeneous and solve it asked Mar 17 in Differential Equations by Takshii ( 346k points) differential equations Jhun Vert Corrections y(9x − 2y)dx − x(6x − y)dy = 0 Let y = vx dy = v dx x dv vx(9x − 2vx)dx − x(6x − vx)(vdx xdv) = 0 vx(9x − 2vx)dx − vx(6x − vx)dx − x2(6x − vx)dv = 0 vx(3x − vx)dx − x2(6x − vx)dv = 0
Set u = x y Hence d u d x = x d y d x y Hence your equation became x u d u d x − 1 = 1 2 u u − 1 u − 1 3 u 2 d u = 1 x d x Now you can integrate both sides You can then integrate both sides To write this as a fuction of y requires the Lambert W function IFor the differential equation `(x^2y^2)dx2xy dy=0`, which of the following are true (A) solution is `x^2y^2=cx` (B) `x^2y^2=cx` `x^2y^2=xc` (D) `ySimplifying (x y) * dx (x 1y) * dy = 0 Reorder the terms for easier multiplication dx (x y) (x 1y) * dy = 0 (x * dx y * dx) (x 1y) * dy = 0 Reorder the terms (dxy dx 2) (x 1y) * dy = 0 (dxy dx 2) (x 1y) * dy = 0 Reorder the terms for easier multiplication dxy dx 2 dy (x 1y) = 0 dxy dx 2 (x * dy 1y * dy) = 0 dxy dx 2 (dxy 1dy 2) = 0 Reorder the terms dxy dxy dx 2 1dy 2 = 0 Combine like terms dxy dxy = 2dxy 2dxy dx
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Solution for (3x^2y)dx (x^2yx)dy=0 equation Simplifying (3x 2 y) * dx (x 2 y 1x) * dy = 0 Reorder the terms for easier multiplication dx (3x 2 y) (x 2 y 1x) * dy = 0 (3x 2 * dx y * dx) (x 2 y 1x) * dy = 0 Reorder the terms (dxy 3dx 3) (x 2 y 1x) * dy = 0 (dxy 3dx 3) (x 2 y 1x) * dy = 0 Reorder the terms dxy 3dx 3 (1x x 2 y) * dy = 0 Reorder the terms for easier multiplication dxy 3dx 3 dy (1x x 2 y) = 0 dxy 3dx 3 (1x * dy x Solve this differential equation $$(xy^3 y)dx 2(x^2y^2 x y^4)dy = 0$$ I tried converting it to the form $\frac{dy}{dx} yp(x) = q(x)$ but couldn't The equation is also not homogeneous Keeping $\frac{dy}{dx}$ on one side will not render the numerator as the derivative of the denominator (with some manipulation) on the other side of We are asked to solve the differential equation (x − y) dy dx = x 2y We rearrange a little dy dx = x 2y x −y dy dx = 1 2(y x) 1 − (y x) (I) While I may not need to mention this, this differential equation is what is called a homogeneous differential equation I'll
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Factor out the Greatest Common Factor (GCF), 'd' d(3x x 2 1y y 2) = 0 Subproblem 1 Set the factor 'd' equal to zero and attempt to solve Simplifying d = 0 Solving d = 0 Move all terms containing d to the left, all other terms to the rightThe equation can be written as M(x,y)dx N(x,y)dy = 0 with M = x^2 y^2 1 , N = x^2 2xyThis is not exact because M_y = 2y # N_x = 2(x y) However (M_y N_x)/N = 2/x depends only on x ,Then the integrating factor can be obtained as IF = 1/x^2 One obtains a new equation which is P(x,y)dx Q(x,y)dy =0, with P = 1 y^2/x^2 1/x^22 1 (x y 2 x) d x (y − x 2 y) d y = 0 https//wwwtigeralgebracom/drill/21(xy~2_x)dx_(yx~2y)dy=0/ 21(xy2x)dx(yx2y)dy=0 One solution was found d = 0 Step by step solution Step 1 Step 2 Pulling out like terms 21 Pull out like factors y
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Simple and best practice solution for (x^2yy^2)dxx^3dy=0 equation Check how easy it is, and learn it for the future Our solution is simple, and easy to understand, so don`t hesitate to use it as a solution of your homework If it's not what You are looking for type in the equation solver your own equation and let us solve it Solve (1 xy)y dx x(1 – xy)dy = 0 differential equations;Share It On Facebook Twitter Email 1 Answer 1 vote answered by KumariMuskan (339k points) selected by Nakul01 Best answer The given differential equation is (1 xy)ydx x(1 – xy)dy = 0
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First rearrange the equation x^2\ dyy^2\ dxxy^2(xy)\ dy=0 It can be written as x^2xy^2(xy)\ dy=y^2\ dx \Rightarrow\frac{x^2}{y^2}x^2xy\ dy=dxThe ODE is homogeneous ODE of order one This is because the coefficients of dx and dy are both homogeneous two variables functions of the same order I suggest you write the ODE as y′ = 32t2t2−t−2 = f (t), (x = 0,t = y/x) Find the solution of (xy^22x^2y^3)dx (x^2yx^3y^2)dy=0Solve mathy \, dx (xx^2y) \, dy = 0 \tag*{}/math mathy \, \dfrac{dx}{dy} (xx^2y) = 0 \tag*{}/math mathy \, \dfrac{dx}{dy} x = x^2y \tag*{}/math
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To find the opposite of d x 2 y d x, find the opposite of each term xdydy^ {2}dx^ {2}ydx=0 x d y − d y 2 − d x 2 − y d x = 0 Combine xdy and ydx to get 0 Combine x d y and − y d x to get 0 dy^ {2}dx^ {2}=0 − d y 2 − d x 2 = 0 Combine all terms containing d Combine all terms containing dSee the answer See the answer See the answer done loading(X 2y) Dx − (2x − Y) Dy = 0 Department of PreUniversity Education, Karnataka PUC Karnataka Science Class 12 Textbook Solutions Important Solutions 985 Question Bank Solutions Concept Notes & Videos 466 Syllabus Advertisement Remove all ads
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4 y(8x9y)dx 2x(x3y)dy = 0 substitute y=vx, v is a function of x substitute back v=y/x isolate y Answer 6 2(2y 2 5xy2y4)dxx(2x2y1)dy=0 let y be the dependent variable Divide by dx substitute dy/dx with y' Rewrite in the form of an exact differential equation if the conditions are met, then The general solution is Ψ(x,y)=C 1 If you start using y = z x y ′ = z ′ x − z x 2 the differential equation becomes ( z − 1) z ′ 2 z x = 0 which seems to be easily workable since you can write it as x ′ = − x ( z − 1) 2 z I am sure that you can take it from here If you go to the end, you would have the opportunity to admire a beautiful functionSee the answer solve the equation (3x^2 y) dx ( x^2y x ) dy = 0 Best Answer 100% (1 rating) Previous question Next question
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Equations Tiger Algebra gives you not only the answers, but also the complete step by step method for solving your equations (2x^2y)dx(x^2yx)dy=0 so that you understand betterSolve ( x 2 y − 2 x y 2) d x − ( x 3 − 3 x 2 y) d y = 0 written 34 years ago by smitapn612 ♦ 90 modified 15 months ago by sanketshingote ♦ 570 ADD COMMENT 1 Answer 1 658 views written 34 years ago by smitapn612 ♦ 90 modified 33 years ago by awariswati1 ♦ 770 Solve (y√(x^2y^2))dxxdy=0 Latest Problem Solving in Differential Equations More Questions in Differential Equations Online Questions and Answers in Differential Equations
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View this answer Given 2xy dx(x2−1) dy = 0 2 x y d x ( x 2 − 1) d y = 0 Rewrite 2xy dxx2 dy−1 dy = 0 2 x y d x x 2 d y − 1 d y = 0 Change the sides $$2 xy \ dx x^2 \ dy = 1Simple and best practice solution for (2x^2y)dx(x^2yx)dy=0 equation Check how easy it is, and learn it for the future Our solution is simple, and easy to understand, so don`t hesitate to use it as a solution of your homework If it's not what You are looking for type in the equation solver your own equation and let us solve itLearn how to solve differential equations problems step by step online Solve the differential equation xy*dx(1x^2)dy=0 Grouping the terms of the differential equation Group the terms of the differential equation Move the terms of the y variable to the left side, and the terms of the x variable to the right side Simplify the expression \frac{1}{y}dy Integrate both sides of the
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M(x, y)dx N(x, y)dy = 0 has some special function I(x, y) whose partial derivatives can be put in place of M and N like this ∂I∂x dx ∂I∂y dy = 0 and our job is to find that magical function I(x, yClick here👆to get an answer to your question ️ Solve x^2y dx (x^3 y^3) dy = 0Question Solve The Equation(3x^2 Y) Dx ( X^2y X ) Dy = 0 This problem has been solved!
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Answer to 11) y(y 2x – 1)dx – 2(x y)dy = 0 12) y(2x2 – xy This problem has been solved!To ask Unlimited Maths doubts download Doubtnut from https//googl/9WZjCW Solve `(xy1)dx (2x 2y3)dy=0` Example 15 Show that the differential equation (𝑥−𝑦) 𝑑𝑦/𝑑𝑥=𝑥2𝑦 is homogeneous and solve it Step 1 Find 𝑑𝑦/𝑑𝑥 (𝑥−𝑦) 𝑑𝑦/𝑑𝑥=𝑥2𝑦 𝑑𝑦/𝑑𝑥=((𝑥 2𝑦)/(𝑥 − 𝑦)) Step 2 Put F(𝑥 , 𝑦)=𝑑𝑦/𝑑𝑥 & Find F(𝜆𝑥 ,𝜆𝑦) 𝑑𝑦/𝑑𝑥=((𝑥 2𝑦)/(𝑥 − 𝑦)) Put F(𝑥 , 𝑦)=((𝑥
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To ask Unlimited Maths doubts download Doubtnut from https//googl/9WZjCW Solve `(xy^3y)dx2(x^2y^2xy^4)dy=0`If a homogeneous differential equaiton can be written as dy dx = F (x,y) d y d x = F ( x, y) , where F (x,y) F ( x, y) is a homogeneous function of degree zero, then the differential equation canHelp is appreciated Edit
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Another way to integrate the DE y(1 xy)dx x(1 xy x2y2)dy = 0 (1 xy)(ydx xdy) x3y2dy = 0 (1 xy)dxy x3y2dy = 0 Divide by (xy)3 (1 xy)dxy (xy)3 dy y = 0 Integrate Share edited Dec 16 '19 at 1623 answered Dec 16 '19 at 1510 MtGlasserSolution of the differential equation y(xy 2x2y2)dx x(xy x2y2)dy = 0 is given by (A) 2 logxlogy(1/xy)=C (B) 2 logylogx(1/xy)=C 2Expert Answer 100% (1 rating) The given differential equation is y (x y)dx (x 2y 1)dy = 0 Here m_y = partial differential /partial differential y view the full answer
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