What is the solution for y^{''}+y^'=10x^4+2 ?

The solution for y^{''}+y^'=10x^4+2 is y=c_{1}+c_{2}e^{-x}+2x^5-10x^4+40x^3-120x^2+242x

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y^{''}+y^'=10x^4+2

y^{^{''}} + y^{^{'}} = 10 x^{4} + 2

y = c_{1} + c_{2} e^{- x} + 2 x^{5} - 10 x^{4} + 40 x^{3} - 120 x^{2} + 242 x

Solution steps

y^{''} (x) + y^{'} (x) = 10 x^{4} + 2

Solve linear ODE:

y = c_{1} + c_{2} e^{- x} + 2 x^{5} - 10 x^{4} + 40 x^{3} - 120 x^{2} + 242 x

y = c_{1} + c_{2} e^{- x} + 2 x^{5} - 10 x^{4} + 40 x^{3} - 120 x^{2} + 242 x

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

x^{^{''}} - 4 x = 3 t

\frac{d ^{2} y}{d x ^{2}} - 6 y = e^{3 x} (x^{2} + 2)

2 y^{^{''}} + y^{^{'}} + 2 y = 1, y (0) = 0, y^{^{'}} (0) = 0

y^{^{''}} + y = (sec (x))^{2}

What is the solution for y^{''}+y^'=10x^4+2 ?
The solution for y^{''}+y^'=10x^4+2 is y=c_{1}+c_{2}e^{-x}+2x^5-10x^4+40x^3-120x^2+242x