- #1

kostoglotov

- 234

- 6

1. Homework Statement

1. Homework Statement

In Linear Algebra I'm solving diff eqs with eigenvectors to get all the combinations that will solve for a diff eq.

The text then asked me to check my answer by going back and solving the diff eqs of the system in the usual non-linear algebra way...well, I guess I must have missed something when I learned how to solve first order linear differential equations the first time round, because something I thought was easy has stumped me.

I just need to find all the solutions to [itex]\frac{dy}{dt} - 4y = -6e^{t}[/itex]. Using an integrating factor I get to [itex]y = 2e^{t} + C[/itex]...but this is just one of the solutions. I think I remember only ever getting one answer to these sorts of questions when I did them in my calculus textbook. How do I get the second solution out of this equation.

Without initial conditions I should get [itex]y = c_1 e^{t} + c_2e^{4t}[/itex], with initial conditions [itex]y(0) = -5[/itex] it should become [itex]y = 2e^{t} + 3e^{4t}[/itex]

How do I get this second solution (without using linear algebra)? Using the integrating factor method only gives me the first solution.