solve the following initial value problem y''+4y'=g(t),y(0)=0,y' (0)=1 if g(t) is the function which is 1...

solve the following initial value problem y''+4y'=g(t),y(0)=0,y' (0)=1 if g(t) is the function which is 1 on [0,1) and zero elsewhere

Expert Solution

milcah answered 2 years ago

Solve the initial value problem: y'' + 4y' + 4y = 0; y(0) = 1, y'(0)...

Solve the initial value problem: y'' + 4y' + 4y = 0; y(0) = 1, y'(0) = 0. Solve without the Laplace Transform, first, and then with the Laplace Transform.

Solve the initial value problem: Y''-4y'+4y=f(t) y(0)=-2, y'(0)=1 where f(t) { t if 0<=t<3 , t+2...

Solve the initial value problem: Y''-4y'+4y=f(t) y(0)=-2, y'(0)=1 where f(t) { t if 0<=t<3 , t+2 if t>=3 }

Solve the following initial value problem. y(4) − 5y′′′ + 4y′′ = x, y(0) = 0, y′(0) ...

Solve the following initial value problem. y(4) − 5y′′′ + 4y′′ = x, y(0) = 0, y′(0) = 0, y′′(0) = 0, y′′′(0) = 0.

use laplace transform to solve the initial value problem: y''+4y=3sint y(0)=1, y'(0)=-1

Solve the laplace transform to solve the initial value problem. y"-6y'+9y=t. Y(0)=0, y'(0)=1

Solve the following differential equation: y''+4y'+4y=u(t-1)-u(t-3), y(0)=0, y'(0)=0

Take the Laplace transform of the following initial value and solve for Y(s)=L{y(t)}: y′′+4y={sin(πt) ,0, 0≤t<11≤t...

Take the Laplace transform of the following initial value and solve for Y(s)=L{y(t)}: y′′+4y={sin(πt) ,0, 0≤t<11≤t y(0)=0,y′(0)=0 Y(s)= ? Hint: write the right hand side in terms of the Heaviside function. Now find the inverse transform to find y(t). Use step(t-c) for the Heaviside function u(t−c) . y(t)= ?

Solve the following initial value problem: y'''-4y''+20y'=-102e^3x, y(0)=3, y'(0)=-2, y''(0)=-2

Consider the following initial value problem. y''−4y = 0, y(0) = 0, y'(0) = 5 (a)...

Consider the following initial value problem. y''−4y = 0, y(0) = 0, y'(0) = 5 (a) Solve the IVP using the characteristic equation method from chapter 4. (b) Solve the IVP using the Laplace transform method from chapter 7. (Hint: If you don’t have the same ﬁnal answer for each part, you’ve done something wrong.)

Use Laplace transforms to solve the initial value problem: y''' −y' + t = 0, y(0)...

Use Laplace transforms to solve the initial value problem: y''' −y' + t = 0, y(0) = 0, y'(0) = 0, y''(0) = 0.

Question