What is the solution for y^{''}-14y^'+49y=3t^{-1}e^{7t} ?

The solution for y^{''}-14y^'+49y=3t^{-1}e^{7t} is y=c_{1}e^{7t}+c_{2}te^{7t}-3e^{7t}t+3e^{7t}tln(t)

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y^{''}-14y^'+49y=3t^{-1}e^{7t}

y^{^{''}} - 14 y^{^{'}} + 49 y = 3 t^{- 1} e^{7 t}

y = c_{1} e^{7 t} + c_{2} t e^{7 t} - 3 e^{7 t} t + 3 e^{7 t} t ln (t)

Solution steps

y^{''} (t) - 14 y^{'} (t) + 49 y = 3 t^{- 1} e^{7 t}

Solve linear ODE:

y = c_{1} e^{7 t} + c_{2} t e^{7 t} - 3 e^{7 t} t + 3 e^{7 t} t ln (t)

y = c_{1} e^{7 t} + c_{2} t e^{7 t} - 3 e^{7 t} t + 3 e^{7 t} t ln (t)

\frac{d}{d x} (2 csc (x) + 4 cot (x))

(- 3, 4), (2, - 9)

\int tan^{- \frac{3}{2}} (x) sec^{4} (x) d x

\frac{d y}{d x} = (1 + y^{2}) tan (x)

What is the solution for y^{''}-14y^'+49y=3t^{-1}e^{7t} ?
The solution for y^{''}-14y^'+49y=3t^{-1}e^{7t} is y=c_{1}e^{7t}+c_{2}te^{7t}-3e^{7t}t+3e^{7t}tln(t)