1 point Solve the initialvalue problem dydxe4x5y y01Solution

(1 point) Solve the initial-value problem

dydx=e4x5y, y(0)=1.

Solution

ODE is

y\'+5y=e^{4x}

Integrating factor is e^{5x} Multiplying by this factor gives

y\' e^{5x}+5y e^{5x}=e^{9x}

(y e^{5x})\'=e^{9x}

Integrating gives

y e^{5x}=e^{9x}/9+C

y=e^{4x}/9+Ce^{-5x}