Question

Find the image of the given function or family of functions under the given linear differential operator.

1. y = t³−t,L[y]=y ′′+2y

Answer 1

To find the image of the given function y = t³−t under the linear differential operator L[y]=y′′+2y, we need to apply the operator to the function. The image is 2t³−4t.

Step-by-step explanation:

To find the image of the given function y = t³−t under the linear differential operator L[y]=y′′+2y, we need to apply the operator to the function. First, let's find the second derivative of y, which is y''=6t. Now, substitute this into L[y] to get L[y] = 6t + 2(t³−t) = 2t³−4t.

So, the image of the given function y = t³−t under the linear differential operator L[y]=y′′+2y is 2t³−4t.