Sometimes the solution of one constant coefficient linear di

Sometimes the solution of one constant coefficient linear differential equation will become part of the statement of another such equation. In this case, using Laplace transforms and leaving everything in the frequency domain until the very end is often easiest. Solve the following for y(you don\'t need to give x).

dx/dt+4x=exp(t), x(0)=0

dy/dt+2y=x(t), y(0)=0

Solution

dx/dt+4x=exp(t), x(0)=0

dy/dt+2y=x(t), y(0)=0