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

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

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

\frac{d ^{2} y}{d x ^{2}} + y = x

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

Solution steps

\frac{d ^{2} y}{d x ^{2}} + y = x

Solve linear ODE:

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

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

y^{^{''}} - 4 y = 4 x^{2} e^{2 x}, y (0) = 0, y^{^{'}} (0) = 0

y^{^{''}} + 9 y = \frac{1}{( cos ( 3 x ) )}, y (0) = 0, y^{^{'}} (0) = 0

y^{^{''}} - 25 y = 2

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

y^{^{''}} - 2 y^{^{'}} - 15 y = 4

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