Solve the following initial value: y ''+ 4y = 2 cos 2t, y(0) = −2 and...

Solve the following initial value: y ^''+ 4y = 2 cos 2t, y(0) = −2 and y 0 (0) = 0

Expert Solution

Colby Messinger answered 1 year 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 following initial value problems y'' + y = 2/cos x , y(0) = y'(0)...

Solve the following initial value problems y'' + y = 2/cos x , y(0) = y'(0) = 2 x^3 y''' − 6xy' + 12y = 20x^4, x > 0, y(1) = 8/3 , y'(1) = 50/3 , y''(1) = 14 x^2 y'' − 2xy' + 2y = x^2, x > 0, y(1) = 3, y'(1) = 5

Solve the initial value problem: y'' + y = cos(x) y(0) = 2 y'(0) = -3...

Solve the initial value problem: y'' + y = cos(x) y(0) = 2 y'(0) = -3 y' being the first derivative of y(x), y'' being the second derivative, etc.

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

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.

Solve using Laplace Transform: 1) y'' - 2y' + 5y = cos(2t) - cos(2t)u4pi(t); y(0) =...

Solve using Laplace Transform: 1) y'' - 2y' + 5y = cos(2t) - cos(2t)u4pi(t); y(0) = 0, y'(0) = 0

Solve y′′ + 4y′ + 3y = 15e^2t given y(0) = −7,y′(0) = 16 by the...

Solve y′′ + 4y′ + 3y = 15e^2t given y(0) = −7,y′(0) = 16 by the method of Laplace transforms.

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 }

Question 3 (2 marks) Use Laplace transform to solve the following initial-value problem. y'+y=?^-2t , y(0)=5

Question 3 Use Laplace transform to solve the following initial-value problem. y'+y=?^-2t , y(0)=5

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.)

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