Find the General Solution dy dr = y? – 3y²cos (x) 1.

Q: The particular solution of y(x+y)dx + (x +2y- 1)dy=0; y(0) = 2 by NEDE is

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Q: Show that y(t) =t-2 ln t is a solution to ty"+5ty' +4y 0. (where t> 0)

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Q: dx dt dy dt х — 2у + t х — у + 2t

A: The given equation is dxdt=x-2y+tdydt=x-y+2t This equation can be rewritten as x'=x-2y+t t=x'-x+2y…

Q: Find the general solution of

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Q: dy =, with initial condition y(0) =2 is dx y The solution of %3D

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Q: Find the General and Particular solution of dy/dx = 4y ; y = 3, when x = 0

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Q: Solve the homogeneous DE 3xy dx + (x^2 + y^2) dy = 0.

A: We will take the substitution y=vx, to convert it into separable variable form.

Q: A particular solution of 4x² dy dx dy 4 is vx +8.x- +y = de

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Q: Given the initial condition y(0) = 1, find the particular solution of the equation

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Q: Find the particular solution of the initial value problem: dy 3x2(y? + 1), dx y(0) = 1 %3D

A: We can find the answer as below.

Q: Find the general solution of (y² + 2y) sin æ²dæ + dy = 0. y+1

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Q: Apply classical fourth-order Runge-Kutta method to solve dy dx f(x,y) == 4e®** –0.3y , using h=0.5…

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Q: I. FIND THE GENERAL SOLUTION OF THE FOI dy dy = xy + 3x - 3x dx 1. dx

A: As per our guidelines we are supposed to answer only one question

Q: Obtain the general solution by separating variables. SHOW YOUR SOLUTIONS. xcos2y dx + tany dy = 0

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Q: A: Compute dy at (2, 1) where y = xcos2x dx B: Solve for x: a2 (y³ + vx-4 +y sin2x) < 4cos2r Тдхду…

A: Please see the answer below.

Q: Obtain the General Solution of dx + xydy = y²dx + ydy.

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Q: x'e* cos 3xdx + -dy = 0 Vỹ - 1 %3D

A: In this question, we solve the separable differential equation by direct integral. the differential…

Q: c) Obtain a general solution of + ! dy dx Y = sin x.

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Q: Find the particular solution to DE:  ( xy^2 - x ) dx - ( 2x^2y - 3y ) dy = 0 ; y ( 1 ) = 2

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Q: The trial solution for the non-homogeneous equation d²y +3. dx? dy – 4y = (x³ + x)e* is %3D dx

A: Trial solution: - Assume the differential equation's right side, f(x), is a linear combination of…

Q: 4. Solve the 2nd-order Homogeneous D.E. y" – 36y = 0

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Q: Solve the given initial-value problem. dy 3D х+ 4y, у(0) %3D 6 dx y(x) =

A: Given that dydx=x+4y , and y(0)=6We need to find the solution of above differential equation.

Q: Solve for the general solution of the given non-exact DE. (2y2 + 3xy – 2y +6x)dx + x(x + 2y – 1)dy =…

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Q: 2. (y + 1)dx + (4x – 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: 1. Solve for y, using the method of successive approximation. dy dx = x + y; y(1) = 1

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Q: dy dx ycos X こ y(o)=1 I +2y2

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Q: Find an implicit solution to the initial value proble dy = y? – 2y, dx y(1) = 3. -

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Q: Find the general solution of the DE dy/dx = y(x – y) / x^2

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Q: Solve the general Solution of:  (xsiny/x- ycosy/xdx)dx + xcosy/x dy=0

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Q: 3. Solve the problem y(t) – y(t) = 4t with initial condition y(0) behavior of the solution as t → o…

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Q: solve the first order homogeneous  equation  dy/dx =y/x +(x/y) ^2 , given y(1) =2

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Q: Find the particular solution to DE:  2xy dx = ( x^2- 2y^3 ) dy ; y ( 0 ) = -2

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Q: dy +y=(x-1)y' dx

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Q: 2. Find the particular solution of (xy + x)dx = (x?y² + x² + y² + 1)dy satisfying the initial…

A: Using Variable Separable Method

Q: Find the general solution of the DE (x + y)dx + (x - y)dy =0.

A: Given differential equation is(x+y)dx+(x-y)dy=0Here, M=x+y and N=x-ythen ∂M∂y=1 and…

Q: (4x*y³ + }) dx + (3x*y² –-;) dy = 0 for x(e) = 1 %3D

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Q: 3. y'(x'y-2)dx+x(x*y' + 2y° - x)dy = 0 : y(1) = 1

A: We have to find the particular solution.

Q: 6) 3x²y dx + (x² + y²) dy = 0 3

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Q: dx 2x - y dt dy

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Q: solve the differential equation with the given initial condition.

A: Given:  The differential equation .

Q: . Is sin y x² dx + ydy = 0 a linear?  2. Is y' = y+x / x a homogeneous Equation?

A: We have to check whether the given differential equations are linear and homogeneous or not. A…

Q: dy %3D 3 e*y* dx +

A: Givendydx+y3=exy4To Find:Solution of a given Bernoulli's equation

Q: Find the general solution of the given equations below: 1) dy dy 3+ 2y = e' sin(t) dt

A: Hello, thanks for your question but according to our policy I am answering the very first question.…

Q: Use Separation of Variables to solve the initial value problem. dy : (1 + y²) tan z, y(0) = v3 xp

A: solution of the given equation is tan-1y + log(cos(x)) = π3 detailed solution is given below

Q: Find an explicit solution of the given initial-value problem. y? dx - V1- x² dy = 0, y(0) = %3D

A: detailed explanation below

Q: Find the general solution to the following DE. y +x² dy = 0 dx

A: Given DE, y2+x2dydx=0

Q: The particular solution of y(x+ y)dx + (x+ 2y- 1)dy=0; y(0)= 2 by NEDE is

A: Let's find.

Q: Find the general solution of D.E. below: (x-2y) dx + (2x+y) dy = 0

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