What is the solution for y^{''}-10y^'+25y=6x^2e^{5x} ?

The solution for y^{''}-10y^'+25y=6x^2e^{5x} is y=c_{1}e^{5x}+c_{2}xe^{5x}+(e^{5x}x^4)/2

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y^{''}-10y^'+25y=6x^2e^{5x}

y^{^{''}} - 10 y^{^{'}} + 25 y = 6 x^{2} e^{5 x}

y = c_{1} e^{5 x} + c_{2} x e^{5 x} + \frac{e ^{5 x} x ^{4}}{2}

Solution steps

y^{''} (x) - 10 y^{'} (x) + 25 y = 6 x^{2} e^{5 x}

Solve linear ODE:

y = c_{1} e^{5 x} + c_{2} x e^{5 x} + \frac{e ^{5 x} x ^{4}}{2}

y = c_{1} e^{5 x} + c_{2} x e^{5 x} + \frac{e ^{5 x} x ^{4}}{2}

What is the solution for y^{''}-10y^'+25y=6x^2e^{5x} ?
The solution for y^{''}-10y^'+25y=6x^2e^{5x} is y=c_{1}e^{5x}+c_{2}xe^{5x}+(e^{5x}x^4)/2