What is the solution for y^{''}-6y^'+9y=e^{3t} ?

The solution for y^{''}-6y^'+9y=e^{3t} is y=c_{1}e^{3t}+c_{2}te^{3t}+(e^{3t}t^2)/2

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y^{''}-6y^'+9y=e^{3t}

y^{^{''}} - 6 y^{^{'}} + 9 y = e^{3 t}

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

Solution steps

y^{''} (t) - 6 y^{'} (t) + 9 y = e^{3 t}

Solve linear ODE:

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

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

\int \frac{1}{5 + 2 t} d t

\frac{\partial}{\partial a} (\frac{a ^{3} b ^{4}}{c ^{2} d ^{4}})

2 (x - y) d x + d y = 0

x \to 1 + lim ((x)^{\frac{1}{1 - x}})

x + ∣ x ∣

What is the solution for y^{''}-6y^'+9y=e^{3t} ?
The solution for y^{''}-6y^'+9y=e^{3t} is y=c_{1}e^{3t}+c_{2}te^{3t}+(e^{3t}t^2)/2