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

The solution for y^{''}-2y^'+y=6e^x is y=c_{1}e^x+c_{2}xe^x+3x^2e^x

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

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

y = c_{1} e^{x} + c_{2} x e^{x} + 3 x^{2} e^{x}

Solution steps

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

Solve linear ODE:

y = c_{1} e^{x} + c_{2} x e^{x} + 3 x^{2} e^{x}

y = c_{1} e^{x} + c_{2} x e^{x} + 3 x^{2} e^{x}

\int_{0}^{4} 5 x - x^{2} - x d x

\frac{\partial}{\partial x} (ln (5 + x^{2} y^{2}))

\int 3 x + \frac{1}{x} - \frac{1}{x} d x

\int \frac{1}{x x ^{2} - 25} d x

h \to 0 lim (\frac{3 ^{h} - 1}{h})

What is the solution for y^{''}-2y^'+y=6e^x ?
The solution for y^{''}-2y^'+y=6e^x is y=c_{1}e^x+c_{2}xe^x+3x^2e^x