Solve each of the following differential equations. Find the explicit solution. d²x dx dt 2. cost =-2 sin t dt?

Q: =-4t°y+3et"; y(0)=1 dt

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

Q: Determine the solutions of this differential equation where steps are thorough and explained dy/dx=…

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Q: . Find the general solution of the given differential equations: y' = x°y+ x°y² .3.2

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Q: y " – y = x²e*

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Q: 7. solve the following differential equation. (16y - xy) dx +x dy = 0

A: To solve the given differential equation.

Q: 9. 10. 2ss" + (s')² = 0 2ste tds +(s²e-t-t)dt = 0

A: As per our guidelines we are supposed to answer only first question . Kindly repost other parts in…

Q: 5. y' = (x + y)²

A: Given: y'=(x+y)2

Q: dy y- x у — 3) dx у+x

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Q: x²y² dy — 3у +1 dx

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Q: = e-2x sin2x, y(0) = 1,

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Q: dy Зх + 2у dx Зх + 2у — 1 ||

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Q: dy = 3y +1 xʻy dx ,2

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Q: The general solution of the differential equation dz +6y sin 4z is

A: We need to solve the differential equation d2ydx2+6y=sin 4x The solution of this differential…

Q: 5. y+2y +5y 0 6. y'+12y + 36 y = 0

A: 5)

Q: D. Solve the given differential equation by variations of parameters. 1. y" + y = cos² 2. y" + 2y +…

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Q: Solve the initial value problem: xy' – 2y = x³ sin(2x) – 8x®, y(0) = 8 (Explain the summary of steps…

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Q: Find the general solution of the given second-order differential equation. 3y" + 2y' + y = 0 y(x) =…

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Q: 7. y'+3y +4y 0 8. y'-2y+4y 0 %3D

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Q: 3. Find a general solution to the differential equation. y" - 10y' +25y =t-3 e 5t

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Q: Please help me with this differential equations problem and please show the full solution. Thank you…

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Q: Please help me solve this differential equation and identify P(x), Q(x) and v(x).

A: First we rearrange the equation and find P(x) and Q(x)

Q: 8. dy/dx -y+ ( x² + 2x ) y² = 0

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Q: dx + (x-y + 2)°dy = 0 4.

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Q: 5. (x+4y) dy-y dx = 0

A: Given : Diffrerential Equation (x + 4y3)dy - y dx = 0   To find : General solution of given…

Q: (ycosx + 2xe') + (sinx + x²e° – 1) = 0 dx

A: We have to solve the following differential equation -  ycosx+2xey+sinx+x2ey-1dydx=0

Q: dy dx х +4 1 у 4. Find the general solution of + 5(x + 4)y7

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Q: (10x* + 2y)dx+(4xy+15e")dy = 0, y(1)=0

A: To solve the given differential equation- 10x4+2y2dx+4xy+15e5ydy=0 , y(1)=0 Here we will use the…

Q: (1+y + xy%) dx + (x* y +y + 2Xy) dy = 0

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Q: 4) y"+ y = cos²x

A: The solution is given as

Q: Solve the differential equation y"ty=tan'x

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Q: 3. y' -6y +9y = 0 4. y'+y- 2y = 0

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Q: Use the method of your choice to find the general solution of the following differential equation.

A: y'(t)=yt ∫xndx=xn+1n+1+C

Q: C. Solve the given differential equation by undetermined coefficients. 1. y" + 6y +9y=-xe4 2. y(4)…

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Q: 3. у(х + у)dх + (x + 2у — 1)dy 3D 0

A: Given: y(x+y)dx+(x+2y-1)dy=0

Q: y =Cjx +Cze* %3D

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Q: blve |x+ ye* |dx - хе* dy —D 0, y(1)-0

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Q: dy (3x²y-6x) (x³ +2y) dx ||

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Q: Solve dy dx x+ V xy

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Q: 2xe2"dy + (e?y – 12x?)dx = 0

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Q: dy — 2хе* — у + 6х? dx у+ бх2

A: We will find out the required general solution.

Q: Find the general solution of the following differential equation. r*dy + (25x'y – 5y In r)dr 0

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Q: y" - 3y +2y = 12e3*. (Use method of variation of parameters) %3D

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Q: y(x) = c + cze²2x + C3xe2 + e¬ [c4 cos(3x) + c5 sin(3x)] %3D

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Q: (D³ + 3D² – 4D – 12)y = 0

A: To solve the given differential equation.D3+3D2-4D-12y=0

Q: . Solve for the differential equations and get the general solution. Simplify your answer free from…

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Q: 9. y+2y 0 10. y) – 8y' +16y = 0

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Q: dy *+ 3y = 3x²e-3x dx

A: Explanation of the answer is as follows

Q: Q1: Find the general solution of the differential equation y(4) – 16y : sin 2x + cos 2x.

A: General solution is sum of complementary function and particular Integral. Here Auxiliary equation…

Q: dy 1) dx = y(xy³ – 1)

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Q: To solve the differential equation 3 + ty = sint, y(0) =5 by the 4th order dt %3D Runge-Kutta…

A: standard form for Runge-Kutta method for solving first order differential equation is: dydx = f(t,…