For each of the following initial value problems verify that the accompanying function is a solution: Function: y=xe x + e x A second-order ordinary differential equation d^2y/dx^2 - 2 dy/dx + y = 0 with initial conditions y(0) = 1 and y'(0) = 2.

Q9 of 462 Page 22

For each of the following initial value problems verify that the accompanying function is a solution:

Function: y=xe^x + e^x

Verification:

Y = x e^x + e^x

Differentiating both sides we get,

Therefore, e^x + xe^x is the solution of the differential equation.

For each of the following initial value problems verify that the accompanying function is a solution:

Function: y = e^x + e^-x

For each of the following initial value problems verify that the accompanying function is a solution:

Function: y = e^x+e^2x

Solve the following differential equations