For each of the following initial value problems verify that the accompanying function is a solution: Function: y = e x +e 2x A second-order ordinary differential equation d^2y/dx^2 - 3 dy/dx + 2y = 0 with initial conditions y(0) = 2 and y'(0) = 3.

Q8 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^2x

Verification:

y = e^x + e^2x

Differentiating both sides we get,

Therefore, e^x + e^2x is the solution of the differential equation.

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

Also at x=0, we get y¹=e⁰+2e⁰=3.

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^-x

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

Function: y=xe^x + e^x

Solve the following differential equations