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

The solution for (d^2y)/(dx^2)-(dy)/(dx)=cos(2x) is y=c_{1}e^x+c_{2}-1/10 sin(2x)-1/5 cos(2x)

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(d^2y)/(dx^2)-(dy)/(dx)=cos(2x)

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

y = c_{1} e^{x} + c_{2} - \frac{1}{10} sin (2 x) - \frac{1}{5} cos (2 x)

Solution steps

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

Solve linear ODE:

y = c_{1} e^{x} + c_{2} - \frac{1}{10} sin (2 x) - \frac{1}{5} cos (2 x)

y = c_{1} e^{x} + c_{2} - \frac{1}{10} sin (2 x) - \frac{1}{5} cos (2 x)

4 y^{^{'''}} - 9 y^{^{''}} + 14 y^{^{'}} - 3 y = x e^{x}

y^{^{''}} + y^{^{'}} + 4 y = cos (3 t)

2 y^{^{'''}} + 2 y = 3 e^{- x}

y^{^{'''}} - y^{^{'}} = x^{2} + 2 x e^{x} + e^{2} x

y^{^{''}} + y - 2 y = 2 t - 40 cos (2 t)

What is the solution for (d^2y)/(dx^2)-(dy)/(dx)=cos(2x) ?
The solution for (d^2y)/(dx^2)-(dy)/(dx)=cos(2x) is y=c_{1}e^x+c_{2}-1/10 sin(2x)-1/5 cos(2x)