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

The solution for y^{''}+y^'-2y=1-2x^2 is y=c_{1}e^x+c_{2}e^{-2x}+x^2+x+1

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

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

y = c_{1} e^{x} + c_{2} e^{- 2 x} + x^{2} + x + 1

Solution steps

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

Solve linear ODE:

y = c_{1} e^{x} + c_{2} e^{- 2 x} + x^{2} + x + 1

y = c_{1} e^{x} + c_{2} e^{- 2 x} + x^{2} + x + 1

t \to 1 lim (sin (π t))

\frac{d}{d j} (3 i + 2 j)

\int_{0}^{1} x (1 - x) sin (nπ x) d x

x^{- 7}

What is the solution for y^{''}+y^'-2y=1-2x^2 ?
The solution for y^{''}+y^'-2y=1-2x^2 is y=c_{1}e^x+c_{2}e^{-2x}+x^2+x+1