What is the solution for y^{''}-12y^'+36y=2te^{6t} ?

The solution for y^{''}-12y^'+36y=2te^{6t} is y=c_{1}e^{6t}+c_{2}te^{6t}+(e^{6t}t^3)/3

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y^{''}-12y^'+36y=2te^{6t}

y^{^{''}} - 12 y^{^{'}} + 36 y = 2 t e^{6 t}

y = c_{1} e^{6 t} + c_{2} t e^{6 t} + \frac{e ^{6 t} t ^{3}}{3}

Solution steps

y^{''} (t) - 12 y^{'} (t) + 36 y = 2 t e^{6 t}

Solve linear ODE:

y = c_{1} e^{6 t} + c_{2} t e^{6 t} + \frac{e ^{6 t} t ^{3}}{3}

y = c_{1} e^{6 t} + c_{2} t e^{6 t} + \frac{e ^{6 t} t ^{3}}{3}

t ln (t) \frac{d r}{d t} + r = 9 t e^{t}

\frac{d}{d x} ((\frac{x - 9}{x + 2})^{\frac{3}{2}})

f (x) = - 9 x^{\frac{1}{3}} + 5, at x = 27

x \to \infty lim (\frac{7}{x} - 9)

\int 45 x^{2} ln (x) d x

What is the solution for y^{''}-12y^'+36y=2te^{6t} ?
The solution for y^{''}-12y^'+36y=2te^{6t} is y=c_{1}e^{6t}+c_{2}te^{6t}+(e^{6t}t^3)/3