What is the solution for y^{''}-2y^'+y=14x^{2/3}e^x ?

The solution for y^{''}-2y^'+y=14x^{2/3}e^x is y=c_{1}e^x+c_{2}xe^x+(63e^xx^{8/3})/(20)

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y^{''}-2y^'+y=14x^{2/3}e^x

y^{^{''}} - 2 y^{^{'}} + y = 14 x^{\frac{2}{3}} e^{x}

y = c_{1} e^{x} + c_{2} x e^{x} + \frac{63 e ^{x} x ^{\frac{8}{3}}}{20}

Solution steps

y^{''} (x) - 2 y^{'} (x) + y = 14 x^{\frac{2}{3}} e^{x}

Solve linear ODE:

y = c_{1} e^{x} + c_{2} x e^{x} + \frac{63 e ^{x} x ^{\frac{8}{3}}}{20}

y = c_{1} e^{x} + c_{2} x e^{x} + \frac{63 e ^{x} x ^{\frac{8}{3}}}{20}

\frac{d ^{2} y}{d x ^{2}} - 5 \frac{d y}{d x} + 6 y = 4 e^{2 x}

y^{^{'''}} - 3 y^{^{''}} + 3 y^{^{'}} - y = t^{2} e^{t}

11 x^{^{''}} + 112.5 x = 5 e^{- t}, x (0) = 0, x^{^{'}} (0) = 0

y^{^{''}} + 3 y^{^{'}} + 2 y = 6 e^{- t}, y (0) = 1, y^{^{'}} (0) = 2

y^{^{''}} - 3 y^{^{'}} + 2 y = t e^{2 t}

What is the solution for y^{''}-2y^'+y=14x^{2/3}e^x ?
The solution for y^{''}-2y^'+y=14x^{2/3}e^x is y=c_{1}e^x+c_{2}xe^x+(63e^xx^{8/3})/(20)