Test the exactness of the following equation then solve the equation: y In(y) dx + (x – Iny)dy = 0 -

Q: dy Using Bernoulli's equation, solve for the general solution of Please show complete dx 2x y…

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Q: Use Picard's method to solve dx - Find y3(1)? -xy, y (0) = 1

A: Solution :-

Q: dy Solve for the value of C in the equation: (1-2x)dx when y(0) - 1 3y3 3

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Q: 3. Show the equation (1+ e*y + xye*)dx + (xe* + 2)dy = 0 is exact and solve it.

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Q: Solve using Bernoulli's Equation. y(6y^2 - x - 1) dx +2x dy = 0

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Q: d²y Find the general solution for- dx² dx

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Q: Using undeterminate coefficien ts, Solve : d'y _q dy =9 e + 82* dx 3 3X 3 dx

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Q: -2y -2y (²²7) dx + e dy = 0 ex + x

A: Different ial eq is homogenous.

Q: Find dy/dæ in terms of t if x = te', y = -2t – 2e dy/dx = %3D

A: topic =derivative

Q: (1+ y²)dx + (x²y + y)dy = 0

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Q: dy e I+ x + ×y +メ dx

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Q: Using Bernoulli's equation , find the solution of DE:  4xy dy/dx = y^2 + x^2 ; initial condition…

A: The solution follows as:

Q: Using an integrating factor solve the equation dy 4 + -y = x dx

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Q: 2. Obtain the general solution using Bernoulli's equation. Simplify your final answer. + x dx - –…

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Solve this completely to answer several questions. dy 4y Consider the equation + = x. dx What is the…

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Q: dx -dy = 0 4. Solve

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Q: Solve the equation 3(y+1)dx-(x+y+3)dy=0

A: Variable separable form of differential equation: dydx=f(x)g(y) Apply variable separable to given…

Q: (1 + y²) dx + (x²y + y) dy = 0.

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Q: Solve the bernoulli equation dx/dy+(2/x)y=-x^2y^2cos(x)

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Q: Test the equation for exactness and solve the equation: (1+ y?)dx + (x²y + y)dy = 0

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Q: z = xy dy x + y = 2x/1-x²y² 2. Using the substitution change the "dx to a separable equation. Hence…

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Q: Solve the differcential equation dy = xy - x, given that y = 2 when x = 0, expressing y in terms of…

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Q: Solve the equation 3(y+1)dx-(x+y +3)dy =0.

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Q: Solve this completely to answer several questions. dy 4y Consider the equation- dx = X. What is the…

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Q: dy XY² Solve, given Y(0) = 3 dX

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Q: x(xy – 1)dx + dy = 0 (Non-exact)

A: Solve differential equation.

Q: Q1) Solve the following equation with Bernoulli equation Method, where x(0) =1 dx x* = 2x dy

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Q: xy dx + e* dy = 0 er?

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Q: Solve the equation 3(y+1)dx-(x+ y +3)dy =0.

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Q: dy 1. Solve the equation x2. +x y= 1. dx

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Q: 4. Solve dx - dy = xy-1 1 o = áp-

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Q: What is the general solution of dx? (1– 2e3 )2

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Q: Solve the exact equation   dy/dx= y/x

A: Given, dydx=yx

Q: dy/dx = y-x-1+(x-y+2)-1  find the general solution of the diffrential equation

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Q: dy 2ху+ бх + (х? — 4) dx Solve

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Q: Solve the Euler equation 2r dy 2.x dx? -3r given that y(1) =1 and y'(1) = 2. +3y 0 dx jntaios

A: To solve given differential equation first we write the auxiliary equation and find the roots and…

Q: z = x+ y dy _ x+ y+2 1. Using substitution solve the equation which satisfies the condition y(1) =1.…

A: Use the given substitution to convert the homogeneous differential equation into separable form then…

Q: X CSC -y|dx + xdy=0. Obtain the general solution of

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Q: Find the general solution, using separation of variables: dy dx

A: The given differential equation is  dydx=e-y-x

Q: Solve the equation 3(y+1)dx-(x+y+3)dy =0.

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Q: Determine the constant A such that the equation (x2 + 3xy) dx + (Ax² + 4y) dy = 0 is exact and solve…

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Q: Substitute y=y1+z  and dy/dx=dy1/dx + dz/dx into  dy/dx = P(x)+Q(x)y+R(x)y2 to get a Bernoulli…

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Q: Given (x² + 2y)dx + (+ 2xy+ 2x) dy = 0. 3 i) Check the exactness of the equation. ii) Based on your…

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Q: Solve the equations by variation of parameters. d2y/dx2 -dy/dx = ex cos x, x> 0

A: d2ydx2-dydx=excosx