What is the solution for (d^3+d)y=6x(2x+1) ?

The solution for (d^3+d)y=6x(2x+1) is y=c_{1}+c_{2}cos(x)+c_{3}sin(x)+4x^3+3x^2-24x

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(d^3+d)y=6x(2x+1)

(d^{3} + d) y = 6 x (2 x + 1)

y = c_{1} + c_{2} cos (x) + c_{3} sin (x) + 4 x^{3} + 3 x^{2} - 24 x

Solution steps

(d^{3} + d) y = 6 x (2 x + 1)

Solve linear ODE:

y = c_{1} + c_{2} cos (x) + c_{3} sin (x) + 4 x^{3} + 3 x^{2} - 24 x

y = c_{1} + c_{2} cos (x) + c_{3} sin (x) + 4 x^{3} + 3 x^{2} - 24 x

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

y^{^{''}} - 2 y^{^{'}} + 5 y = e^{2 x} sin (3 x) - sin (x)

y^{^{''}} - 9 y = cos (3 x)

y^{^{''}} + 9 y = 8 x, y (0) = 1, y^{^{'}} (0) = 3

y^{^{''}} - 8 y^{^{'}} + 16 y = 20 x + 7

What is the solution for (d^3+d)y=6x(2x+1) ?
The solution for (d^3+d)y=6x(2x+1) is y=c_{1}+c_{2}cos(x)+c_{3}sin(x)+4x^3+3x^2-24x