Math Challenges

Submissions for Problem #56

Solve the initial-value problem for y.

\[ \displaylines{\frac{dy}{dt}=-y+\sin2t\\ y\left(0\right)=5} \]

zapwai

Solution: \( \displaylines{\text{Using integrating factors will yield }\\ y=-\frac25\cos\left(2t\right)+\frac15\sin\left(2t\right)+Ce^{-t}\\ y\left(0\right)=-\frac25+C=5\text{ gives }C=\frac{27}{5}} \)