Solve the given initial value problem. y" +81y=0; y(0)=2, y'(0)=4 y(t) =

Q: Solve. y'' – 36y = et The general solution will be 6t 6t y(t) : cje + c2e +

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Q: Find the general solution to y''-1=0

A: y''-1 =0y'' = 1y' = ∫1 dxy' = x + By =∫(x + B) dxy = x22 + Bx + A

Q: e the following nth-order equation using the variation of parameter method: y"-3y"+3y'-y=

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Q: solve the equation :- y'(t) = y(t) [a-y(t) ] ₁ y(0) = a/2, 970

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Q: Use the convolution to write a formula for problem: y" + 25y = f(t), y(0) = -2, y(0) = 1. |

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Q: Solve the ODE  y'+(1/x)y-ex=0, when x>0

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Q: First, solve the following IVP, y' = (15x + yr1 . 15 , y(0)=1. Then calculate y(12).

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Q: Solve the equation y' + 3y = 10 sint, when y(0) two decimal place number. 0. Evaluate f (1) in

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Q: 3. Solve each equation. y(0) = 1, y' (0) = -1 (a) y" + 4y = 0, (b) y" + 5y = 0

A: We have to solve given problem:

Q: Solve: x"(t) + 2x'(t) + x(t) = 3t e-t x(0) = 4, x'(0) = 2 Evaluate: F(2) = Evaluate: f(1) =…

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Q: 2. Use the variation of parameters to solve: y" -2y" + y' = 4e*.

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Q: solve by bernoulli y' + (8/x)y = x6y4

A: We will find out the required general solution for given Bernoulli's equation.

Q: y' = (1 − x²)²; y(15) = 149,645

A: differential equation

Q: 1) y'+ = 5, y(1) = 4 Solve

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Q: Solve y(H) a) Y (6) = y (4) = ? %3D b) y"-y' • 24 ylo)=1;y'(0)=-2 %3D

A: We have to find the solution y(t) from the following  a) y(s)=1s2(s2+1) b) y''-y'=2t, y(0)=1,…

Q: Solve for y. y' = 7x + xy; y = 5 when x= 0 y =

A: We have to solve for y for the given differential equation: y'=7x+xy; y=5 when x=0. Rewriting the…

Q: Consider the equation y' + 5y = 2. Show that the function o given by: %3D 2 $(x) is a solution,…

A: Given y'+5y=2 We have to find ∅x

Q: Solve the y" + 2y + y = x², y(0) = 1, y'(0) = 2.

A: Given initial value problem isWe have to solve the above IVP.

Q: solve y’ – (y/x) = xy2

A: We have to solve differential equations

Q: Calculate the first, second, and third derivatives of y(t) = 2016/5 – 6127. (Use symbolic notation…

A: We will use simple differentiation rules to solve this question.

Q: Solve the initial value problem, and graph the solution function x(t). x' + 10x' +26x =…

A: Given equation contains Dirac delta function we solve by Laplace Transformation.

Q: 3 2t + 3 h(t) = 6 t2 Find h'(t) *

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Q: Find the value of y (0.4) if y' + 0.2y = 0, y(0) = 5. Solve analytically.

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Q: Solve the following IVP. y"'-5y"-22+56=0 y(0)=1 y'(0)=-2 y''(0

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Q: f y=y(x) is the desired solution of 2 = f(x,y), Derive Euler %3D teration formula for solving ODES…

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Q: 6. Solve: y"(t) = te', y(0)=0, y'(0)=1

A: Given data y"(t)=tet  y(0)=0, y'(0)=1