What is the solution for (D^4+D^2)y=18x-4sin(x) ?

The solution for (D^4+D^2)y=18x-4sin(x) is y=c_{1}+c_{2}x+c_{3}cos(x)+c_{4}sin(x)+3x^3-2xcos(x)

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(D^4+D^2)y=18x-4sin(x)

(D^{4} + D^{2}) y = 18 x - 4 sin (x)

y = c_{1} + c_{2} x + c_{3} cos (x) + c_{4} sin (x) + 3 x^{3} - 2 x cos (x)

Solution steps

(D^{4} + D^{2}) y = 18 x - 4 sin (x)

Solve linear ODE:

y = c_{1} + c_{2} x + c_{3} cos (x) + c_{4} sin (x) + 3 x^{3} - 2 x cos (x)

y = c_{1} + c_{2} x + c_{3} cos (x) + c_{4} sin (x) + 3 x^{3} - 2 x cos (x)

y^{^{''}} - 2 y^{^{'}} + 5 y = e^{2 x}

y^{^{'''}} + 9 y^{^{''}} - 108 y = e^{- 6 x}

y^{^{''''}} + 2 y^{^{''}} + y = 3 t + 4

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

\frac{d ^{2} y}{d x ^{2}} + 4 \frac{d y}{d x} + 5 y = e^{x} cos (2 x)

What is the solution for (D^4+D^2)y=18x-4sin(x) ?
The solution for (D^4+D^2)y=18x-4sin(x) is y=c_{1}+c_{2}x+c_{3}cos(x)+c_{4}sin(x)+3x^3-2xcos(x)