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

Q7 of 462 Page 22

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

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

y = e^x + e^-x

Differentiating both sides we get,

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

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

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

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

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

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

Function: y=xe^x + e^x