Find the general solution of the given differential equation 2y"' + 3y' +y= 2 + 3 sint

I suppose you meant to have the second derivative as the first term:

The corresponding homogeneous equation

has characteristic equation

with roots at and , giving the characteristic solution

For the nonhomogeneous equation, assume a solution of the form

with derivatives

Substituting these into the ODE gives

Then the ODE has solution

the answer is 844

step-by-step explanation:

it is 844 because if you add 836.50 + 7.5 you will get 844