What is the solution for (d^2y)/(dx^2)=(4sin(3x)) ?

The solution for (d^2y)/(dx^2)=(4sin(3x)) is y=-4/9 sin(3x)+c_{1}x+c_{2}

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(d^2y)/(dx^2)=(4sin(3x))

\frac{d ^{2} y}{d x ^{2}} = (4 sin (3 x))

y = - \frac{4}{9} sin (3 x) + c_{1} x + c_{2}

Solution steps

\frac{d ^{2} y}{d x ^{2}} = (4 sin (3 x))

Substitute

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

with

y^{''} (x)

y^{^{''}} (x) = (4 sin (3 x))

Solve

y^{''} (x) = 4 sin (3 x) : y^{'} (x) = - \frac{4}{3} cos (3 x) + c_{1}

Solve

y^{'} (x) = - \frac{4}{3} cos (3 x) + c_{1} : y = - \frac{4}{9} sin (3 x) + c_{1} x + c_{2}

y = - \frac{4}{9} sin (3 x) + c_{1} x + c_{2}

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What is the solution for (d^2y)/(dx^2)=(4sin(3x)) ?
The solution for (d^2y)/(dx^2)=(4sin(3x)) is y=-4/9 sin(3x)+c_{1}x+c_{2}