What is the solution for y^{''}-14y^'+49y=t^{-2}e^{7t} ?

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

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y^{''}-14y^'+49y=t^{-2}e^{7t}

y^{^{''}} - 14 y^{^{'}} + 49 y = t^{- 2} e^{7 t}

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

Solution steps

y^{''} (t) - 14 y^{'} (t) + 49 y = t^{- 2} e^{7 t}

Solve linear ODE:

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

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

x \to - \infty lim (\frac{7}{x} - 4)

\int \frac{1}{w ^{3}} d w

12 x + 16 x^{\frac{3}{4}}

f (x) = x^{2} - 4, (- 2, 3)

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

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