What is the solution for (d^2y)/(dx^2)=sin(2x) ?

The solution for (d^2y)/(dx^2)=sin(2x) is y=-1/4 sin(2x)+c_{1}x+c_{2}

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(d^2y)/(dx^2)=sin(2x)

\frac{d ^{2} y}{d x ^{2}} = sin (2 x)

y = - \frac{1}{4} sin (2 x) + c_{1} x + c_{2}

Solution steps

\frac{d ^{2} y}{d x ^{2}} = sin (2 x)

Substitute

\frac{d ^{2} y}{d x ^{2}}

with

y^{''} (x)

y^{^{''}} (x) = sin (2 x)

Solve

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

Solve

y^{'} (x) = - \frac{1}{2} cos (2 x) + c_{1} : y = - \frac{1}{4} sin (2 x) + c_{1} x + c_{2}

y = - \frac{1}{4} sin (2 x) + c_{1} x + c_{2}

What is the solution for (d^2y)/(dx^2)=sin(2x) ?
The solution for (d^2y)/(dx^2)=sin(2x) is y=-1/4 sin(2x)+c_{1}x+c_{2}