What is the solution for y^{''}-7y^{''}+19y^'-13y=0 ?

The solution for y^{''}-7y^{''}+19y^'-13y=0 is y=c_{1}e^t+c_{2}e^{(13t)/6}

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y^{''}-7y^{''}+19y^'-13y=0

y^{^{''}} - 7 y^{^{''}} + 19 y^{^{'}} - 13 y = 0

y = c_{1} e^{t} + c_{2} e^{\frac{13 t}{6}}

Solution steps

y^{''} (t) - 7 y^{''} (t) + 19 y^{'} (t) - 13 y = 0

Solve linear ODE:

y = c_{1} e^{t} + c_{2} e^{\frac{13 t}{6}}

y = c_{1} e^{t} + c_{2} e^{\frac{13 t}{6}}

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

y^{^{''}} - 2 y^{^{'}} + y = 0, y (0) = 8, y^{^{'}} (0) = 3

\frac{d ^{2} y}{d x ^{2}} - 10 \frac{d y}{d x} + 5^{2} y = 0

12 \frac{d ^{2} y}{d x ^{2}} - 5 \frac{d y}{d x} - 3 y = 0

\frac{d ^{2} y}{d x ^{2}} (1) - \frac{d y}{d x} (10) = 0

What is the solution for y^{''}-7y^{''}+19y^'-13y=0 ?
The solution for y^{''}-7y^{''}+19y^'-13y=0 is y=c_{1}e^t+c_{2}e^{(13t)/6}