What is the solution for y^{''}-y=x^2,y(0)=-3,y^'(0)=5 ?

The solution for y^{''}-y=x^2,y(0)=-3,y^'(0)=5 is y=2e^x-3e^{-x}-x^2-2

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y^{''}-y=x^2,y(0)=-3,y^'(0)=5

y^{^{''}} - y = x^{2}, y (0) = - 3, y^{^{'}} (0) = 5

y = 2 e^{x} - 3 e^{- x} - x^{2} - 2

Solution steps

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

Solve linear ODE:

y = 2 e^{x} - 3 e^{- x} - x^{2} - 2

y = 2 e^{x} - 3 e^{- x} - x^{2} - 2

x^{^{''}} - 6 x^{^{'}} + 13 x = 2197 t^{2}

(d^{2} + 1) y = e^{x}

y^{^{''}} + 2 y^{^{'}} + 5 = e^{x}

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

y^{^{''}} = 2 y^{^{'}} + 15 y + sin (3 t)

What is the solution for y^{''}-y=x^2,y(0)=-3,y^'(0)=5 ?
The solution for y^{''}-y=x^2,y(0)=-3,y^'(0)=5 is y=2e^x-3e^{-x}-x^2-2