What is the solution for y^{''}+y=e^{2x},y(0)=0 ?

The solution for y^{''}+y=e^{2x},y(0)=0 is y=-1/5 cos(x)+c_{2}sin(x)+1/5 e^{2x}

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y^{''}+y=e^{2x},y(0)=0

y^{^{''}} + y = e^{2 x}, y (0) = 0

y = - \frac{1}{5} cos (x) + c_{2} sin (x) + \frac{1}{5} e^{2 x}

Solution steps

y^{''} (x) + y = e^{2 x}

Solve linear ODE:

y = - \frac{1}{5} cos (x) + c_{2} sin (x) + \frac{1}{5} e^{2 x}

y = - \frac{1}{5} cos (x) + c_{2} sin (x) + \frac{1}{5} e^{2 x}

What is the solution for y^{''}+y=e^{2x},y(0)=0 ?
The solution for y^{''}+y=e^{2x},y(0)=0 is y=-1/5 cos(x)+c_{2}sin(x)+1/5 e^{2x}