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

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

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(d^2y)/(dx^2)+4y=cos(2x)

\frac{d ^{2} y}{d x ^{2}} + 4 y = cos (2 x)

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

Solution steps

\frac{d ^{2} y}{d x ^{2}} + 4 y = cos (2 x)

Solve linear ODE:

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

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

y^{^{''}} + 9 y^{^{'}} = tan^{3} (x)

\frac{d ^{2} y}{d x ^{2}} + 3 \frac{d y}{d x} + 2 y = cos (x)

y^{^{''}} - y^{^{'}} = 3 - 2 x, y (0) = - 1, y^{^{'}} (0) = - 1

y^{^{''}} - 25 y = e^{x}

y^{^{''}} - 14 y^{^{'}} + 45 y = 360 x^{2} - 224 x + 16

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