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

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

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

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

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

Solution steps

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

Solve linear ODE:

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

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

y^{^{''}} - 4 y^{^{'}} + 5 y = x e^{x}

y^{^{''}} + 2 y^{^{'}} + 5 y = 3 e^{- 2 t}, y (0) = 1, y^{^{'}} (0) = 1

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

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

y^{^{''}} + 100 y^{^{'}} + 2500 y = 30

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