What is the solution for y^{''}+4y=3sin(x)+5cos(3x) ?

The solution for y^{''}+4y=3sin(x)+5cos(3x) is y=c_{1}cos(2x)+c_{2}sin(2x)+sin(x)-cos(3x)

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y^{''}+4y=3sin(x)+5cos(3x)

y^{^{''}} + 4 y = 3 sin (x) + 5 cos (3 x)

y = c_{1} cos (2 x) + c_{2} sin (2 x) + sin (x) - cos (3 x)

Solution steps

y^{''} (x) + 4 y = 3 sin (x) + 5 cos (3 x)

Solve linear ODE:

y = c_{1} cos (2 x) + c_{2} sin (2 x) + sin (x) - cos (3 x)

y = c_{1} cos (2 x) + c_{2} sin (2 x) + sin (x) - cos (3 x)

y^{^{''}} + 4 y = x sin^{2} (x)

y^{^{''}} - 2 y^{^{'}} - 3 y = 4, y (0) = 1, y^{^{'}} (0) = - 1

y^{^{''}} + 5 y^{^{'}} + 6 y = 20 sin (2 t)

y^{^{''}} - 2 y^{^{'}} + y = 25 sin (2 x)

y^{^{''}} - 8 y^{^{'}} + 20 y = 200 x^{2} - 65 x e^{x}

What is the solution for y^{''}+4y=3sin(x)+5cos(3x) ?
The solution for y^{''}+4y=3sin(x)+5cos(3x) is y=c_{1}cos(2x)+c_{2}sin(2x)+sin(x)-cos(3x)