consider the linear diff. eq. u' = p(t)u + q(t). is it true that the sum of two solutions is again a solution? is a constant time a solution again a solution? what if q(t) = 0? show that if u1 is a solution to u' = p(t)u and u2 is a solution to u' = p(t)u + q(t), then u1 + u2 is a solution to u' = p(t)u + q(t).

Question

consider the linear diff. eq. u' = p(t)u + q(t).  is it true that the sum of two solutions is again a solution?  is a constant time a solution again a solution?  what if q(t) = 0?  show that if u1 is a solution to u' = p(t)u and u2 is a solution to u' = p(t)u + q(t), then u1 + u2 is a solution to u' = p(t)u + q(t).

anonymous · Answer

i'm pretty sure this has to do with a simple e^x deal but am not exactly sure how to prove it.