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

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

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(d^2y)/(dx^2)+y=3cos(2x)

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

y = c_{1} cos (x) + c_{2} sin (x) - cos (2 x)

Solution steps

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

Solve linear ODE:

y = c_{1} cos (x) + c_{2} sin (x) - cos (2 x)

y = c_{1} cos (x) + c_{2} sin (x) - cos (2 x)

y^{^{''}} + 2 y^{^{'}} = 3 + sin (t)

y^{^{''}} - 2 y + 10 y = e^{x} cos (3 x)

y^{^{''}} - 8 y^{^{'}} + 7 = 0, y (0) = 1, y^{^{'}} (0) = 2

y^{^{''}} + y^{^{'}} - 2 y = - 10

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

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