What is the solution for y^{''}+y= 1/(x^2) ?

The solution for y^{''}+y= 1/(x^2) is y=c_{1}cos(x)+c_{2}sin(x)-cos(x)\Ci(x)-sin(x)\Si(x)

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y^{''}+y= 1/(x^2)

y^{^{''}} + y = \frac{1}{x ^{2}}

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

Solution steps

y^{''} (x) + y = \frac{1}{x ^{2}}

Solve linear ODE:

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

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

\frac{d ^{2} y}{d t ^{2}} + 2 \cdot \frac{d y}{d t} + 2 y = 11 t^{3}

3 y^{^{''}} + 27 y^{^{'}} + 42 y = 25 sin (t)

y^{^{'''}} - 4 y^{^{'}} = x + 3 cos (x) + e^{- 2 x}

y^{^{''}} - 9 y^{^{'}} + 8 y = x

y^{^{''}} + 14 y^{^{'}} + 50 y = 371 cos (t)

What is the solution for y^{''}+y= 1/(x^2) ?
The solution for y^{''}+y= 1/(x^2) is y=c_{1}cos(x)+c_{2}sin(x)-cos(x)\Ci(x)-sin(x)\Si(x)