What is the solution for y^{''}+y^'-6=4x^3+3x ?

The solution for y^{''}+y^'-6=4x^3+3x is y=c_{1}+c_{2}e^{-x}+x^4-4x^3+(27x^2)/2-21x

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y^{''}+y^'-6=4x^3+3x

y^{^{''}} + y^{^{'}} - 6 = 4 x^{3} + 3 x

y = c_{1} + c_{2} e^{- x} + x^{4} - 4 x^{3} + \frac{27 x ^{2}}{2} - 21 x

Solution steps

y^{''} (x) + y^{'} (x) - 6 = 4 x^{3} + 3 x

Solve linear ODE:

y = c_{1} + c_{2} e^{- x} + x^{4} - 4 x^{3} + \frac{27 x ^{2}}{2} - 21 x

y = c_{1} + c_{2} e^{- x} + x^{4} - 4 x^{3} + \frac{27 x ^{2}}{2} - 21 x

What is the solution for y^{''}+y^'-6=4x^3+3x ?
The solution for y^{''}+y^'-6=4x^3+3x is y=c_{1}+c_{2}e^{-x}+x^4-4x^3+(27x^2)/2-21x