What is the solution for y^{''}+6y^'-16y=7y^'-10y ?

The solution for y^{''}+6y^'-16y=7y^'-10y is y=c_{1}e^{3t}+c_{2}e^{-2t}

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y^{''}+6y^'-16y=7y^'-10y

y^{^{''}} + 6 y^{^{'}} - 16 y = 7 y^{^{'}} - 10 y

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

Solution steps

y^{''} (t) + 6 y^{'} (t) - 16 y = 7 y^{'} (t) - 10 y

Solve linear ODE:

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

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

y^{^{''}} - \frac{n ^{2}}{4} y = 0

\frac{d ^{2} y}{d x ^{2}} + 4 (\frac{d y}{d x}) + 4 y = 0

4 x^{^{''}} + 3 x^{^{'}} + 5 x = 0

y^{^{''}} + 64 y = 0, y^{^{'}} (0) = 0

x^{^{''}} + 2^{2} \cdot 3^{2} x = 0

What is the solution for y^{''}+6y^'-16y=7y^'-10y ?
The solution for y^{''}+6y^'-16y=7y^'-10y is y=c_{1}e^{3t}+c_{2}e^{-2t}