What is the solution for y^{''}-5y^'-6y=12e^{2t} ?

The solution for y^{''}-5y^'-6y=12e^{2t} is y=c_{1}e^{6t}+c_{2}e^{-t}-e^{2t}

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y^{''}-5y^'-6y=12e^{2t}

y^{^{''}} - 5 y^{^{'}} - 6 y = 12 e^{2 t}

y = c_{1} e^{6 t} + c_{2} e^{- t} - e^{2 t}

Solution steps

y^{''} (t) - 5 y^{'} (t) - 6 y = 12 e^{2 t}

Solve linear ODE:

y = c_{1} e^{6 t} + c_{2} e^{- t} - e^{2 t}

y = c_{1} e^{6 t} + c_{2} e^{- t} - e^{2 t}

x \to 0 lim (\frac{1}{( x - 1 ) ^{2}} + 2)

\frac{d y}{d x} + 10 y = 11

\frac{d}{d x} (x^{2} - 4 x + 10)

x \to 5 lim (\frac{1}{x ^{2} - 1})

What is the solution for y^{''}-5y^'-6y=12e^{2t} ?
The solution for y^{''}-5y^'-6y=12e^{2t} is y=c_{1}e^{6t}+c_{2}e^{-t}-e^{2t}