Solve the initial value problem: dy/dt-y=7e^t + 10e^6t with y(0)=4

Question

y = ?

Answer 1

you know that the solution to dy/dt - y = 0 is
y = c e^t
that means that the solution to y'-y=7e^t + 10e^6t is
y = c e^t + 7t e^t + 2e^6t