For each of the following initial value problems verify that the accompanying function is a solution: Function: y=e x +1 The differential equation d^2y/dx^2 - dy/dx = 0 with the initial condition y(0) = 2.

Q4 of 462 Page 22

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

Function: y=e^x+1

Verification:

Y = e^x + 1

Differentiating both sides we get,

Therefore, e^x+1 is the solution of the differential equation.

Also at x=0, we get y=e⁰+1 which is equal to 2.

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

Function:

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

Function: y=sin x

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

Function: y = e^-x+2

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

Function: y = sin x + cos x