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 +

A:

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=

A:

Q: y' = et ; y(0) = 2 find the general solution

A:

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

A:

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

A:

Q: Solve the following equation y" + 2/ + y = * using the method of variation of parameters.

A:

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 for y(x):  y’’ – 5y’ + 12y = 0; y(2) = 0; y’(2) = -4

A:

Q: The general solution of y' = 10 can be written in the form Y =C D

A: We are solving the given problem by using the method of separation of variable.

Q: 1. Solve the equation y2 + 6x = y(3y – 2x)y'

A:

Q: Solve for y: y'=7y²², y = 3 when x = 1

A:

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

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

Q: Solve the following difference equation with initial conditions: 12Yn + Yn+1 = Yn+2, Y₁ = −2, Y₂ =…

A:

Q: Find the particular solution. y' = ex − 8;    y(0) = 9

A: Given, y' = ex − 8

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

A:

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 the following initial value problems: (y + 2y - 3y = u(t-1)-u(t-3), y (0) = 0, y'(0) = -1.

A: The initial value problem is given as y''+2y'-3y=u(t-1)-u(t-3) with initial condition y(0)=0,…

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: .1 Solve the equation x'y"-3xy'+3y 2x'e by method of variation of parameters.

A:

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: Given equation is using Laplace 1- y" - 3y' + 2y = 4e²t y(0)= -3 & v'(0)= -5

A:

Q: Find the general solution of the following equation valid near the origin: (1+4x2)y''-8y=0

A:

Q: Find the general solution of the given equation y''  - 9y = 0

A: From the given data:

Q: Verify that y = x² – 1 is a solution of (y')* + y² = -1. %3D

A: Given;            y=x2-1 is a solution of y'4+y2=-1 We compute the first derivative.…