What is the solution for (d^2y)/(dx^2)+y=4xcos(x) ?

The solution for (d^2y)/(dx^2)+y=4xcos(x) is y=c_{1}cos(x)+c_{2}sin(x)+x^2sin(x)+xcos(x)

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(d^2y)/(dx^2)+y=4xcos(x)

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

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

Solution steps

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

Solve linear ODE:

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

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

y^{^{''}} + 49 y = 3

y^{^{''}} - 16 y = sin (4 x)

x^{^{''}} + x = - e^{t}

\frac{d ^{2} y}{d x ^{2}} + 9 y = 5 sin (4 x)

y^{^{''}} + y = cos (t), y (0) = 1, y^{^{'}} (0) = - 3

What is the solution for (d^2y)/(dx^2)+y=4xcos(x) ?
The solution for (d^2y)/(dx^2)+y=4xcos(x) is y=c_{1}cos(x)+c_{2}sin(x)+x^2sin(x)+xcos(x)