What is the solution for y*u^2-y^{''}=1 ?

The solution for y*u^2-y^{''}=1 is y=c_{1}e^{ut}+c_{2}e^{-ut}+1/(u^2)

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y*u^2-y^{''}=1

y \cdot u^{2} - y^{^{''}} = 1

y = c_{1} e^{u t} + c_{2} e^{- u t} + \frac{1}{u ^{2}}

Solution steps

y \cdot u^{2} - y^{''} (t) = 1

Solve linear ODE:

y = c_{1} e^{u t} + c_{2} e^{- u t} + \frac{1}{u ^{2}}

y = c_{1} e^{u t} + c_{2} e^{- u t} + \frac{1}{u ^{2}}

y^{^{''}} + 4 y^{^{'}} + 4 y = x^{2} e - 2 x + 1

y^{^{''}} - y^{^{'}} = 1 - k x

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

y^{^{''}} = 1 - y, y (0) = 0, y (1) = 0

(4 d^{2} + 12 d + 9) y = 144 e^{- 3} x

What is the solution for y*u^2-y^{''}=1 ?
The solution for y*u^2-y^{''}=1 is y=c_{1}e^{ut}+c_{2}e^{-ut}+1/(u^2)