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^{^{''}} + 6 y^{^{'}} + 5 y = 12 e^{t}, y (0) = - 1, y^{^{'}} (0) = 7

y^{^{''}} - 6 y^{^{'}} + 9 y = x^{2} + e^{x}

D, D (t) = \frac{100 ln ( t + 2 )}{t + 2}

2 y^{^{''}} + 3 y^{^{'}} - 2 y = 6 x^{2} + 5 x - 8

y^{^{''}} + 4 y = 2 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)