y'' - 4y' + 3y = e^-t + t.

The general solution to this is the sum of the general solution to

y'' - 4y' + 3y = 0,

and a particular integral of the original equation.

To find a particular integral look at a trial solution:

y(t) = A e^{-t} + ax^2 + bx +c.

Determine the coefficients by differentiating twice and substituting into

the original equation.

You will now have the general solution and you need only fit the initial conditions to find the solution you require.

RonL