What is the solution for 5y^{''}-10y^'+5y=e^xln(x) ?

The solution for 5y^{''}-10y^'+5y=e^xln(x) is y=c_{1}e^x+c_{2}xe^x+(2e^xx^2ln(x)-3e^xx^2)/(20)

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5y^{''}-10y^'+5y=e^xln(x)

5 y^{^{''}} - 10 y^{^{'}} + 5 y = e^{x} ln (x)

y = c_{1} e^{x} + c_{2} x e^{x} + \frac{2 e ^{x} x ^{2} ln ( x ) - 3 e ^{x} x ^{2}}{20}

Solution steps

5 y^{''} (x) - 10 y^{'} (x) + 5 y = e^{x} ln (x)

Solve linear ODE:

y = c_{1} e^{x} + c_{2} x e^{x} + \frac{2 e ^{x} x ^{2} ln ( x ) - 3 e ^{x} x ^{2}}{20}

y = c_{1} e^{x} + c_{2} x e^{x} + \frac{2 e ^{x} x ^{2} ln ( x ) - 3 e ^{x} x ^{2}}{20}

y^{^{''}} + 5 y^{^{'}} + 6 y = 3 t^{2} + 4

y^{^{''}} + y = sec^{3} (x), y (0) = 1, y^{^{'}} (0) = \frac{1}{2}

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

y^{^{''}} + y = 2, y (0) = 2, y^{^{'}} (0) = 3

y^{^{''}} - y = \frac{4 e ^{- x}}{1 - e ^{- 2 x}}

What is the solution for 5y^{''}-10y^'+5y=e^xln(x) ?
The solution for 5y^{''}-10y^'+5y=e^xln(x) is y=c_{1}e^x+c_{2}xe^x+(2e^xx^2ln(x)-3e^xx^2)/(20)