What is the solution for y^{'''}+y^{''}=3e^x+4x^2 ?

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

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y^{'''}+y^{''}=3e^x+4x^2

y^{^{'''}} + y^{^{''}} = 3 e^{x} + 4 x^{2}

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

Solution steps

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

Solve linear ODE:

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

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

\frac{d y}{d t} - 2 t y = 9 t^{2} e^{t^{2}}

\frac{d y}{d x} = y sin (x), y (0) = 1

\int e^{x y} d x

f (x) = \frac{1 + 16 x ^{2}}{( 4 x ) ^{3}}

y^{^{''}} - y^{^{'}} = 0, y (0) = 10

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