Given: 2y"+ 3y' + y = 13x2 determine yp determine ye ns ) determine the general solution satisfying the following conditions: y' (2) + y" (2) = 2(13 -e1) & 0.5y"(2) + y(2) = 13 +2e-2 ans.

I'm not sure what to make of "yp" and "ye ns", or the given initial conditions, so I'll let you handle that and just focus on the general solution.

The corresponding homogeneous ODE has characteristic equation

with roots at and , so the characteristic solution to the ODE is

For the non-homogeneous ODE, assume a solution of the form

Substituting and its derivatives into the ODE gives

so that the particular solution is

and the general solution is

step-by-step explanation: