What is the solution for 13y^{''}-14y^'+y=0,y(0)=13,y^'(0)= 1/13 ?

The solution for 13y^{''}-14y^'+y=0,y(0)=13,y^'(0)= 1/13 is y=-e^t+14e^{t/(13)}

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13y^{''}-14y^'+y=0,y(0)=13,y^'(0)= 1/13

13 y^{^{''}} - 14 y^{^{'}} + y = 0, y (0) = 13, y^{^{'}} (0) = \frac{1}{13}

y = - e^{t} + 14 e^{\frac{t}{13}}

Solution steps

13 y^{''} (t) - 14 y^{'} (t) + y = 0

Solve linear ODE:

y = - e^{t} + 14 e^{\frac{t}{13}}

y = - e^{t} + 14 e^{\frac{t}{13}}

y^{^{''}} - \frac{1}{4} y = 0

y^{^{''}} + a^{2} \cdot n^{2} \cdot π^{2} \cdot y = 0, y^{^{'}} (0) = 0

\frac{d ^{2} y}{d x ^{2}} + k^{2} \cdot y^{^{'}} = 0

4 y^{^{''}} + 4 y^{^{'}} + 6 y = 0

\frac{d ^{2} y}{d x ^{2}} - 12 \frac{d y}{d x} + 35 y = 0

What is the solution for 13y^{''}-14y^'+y=0,y(0)=13,y^'(0)= 1/13 ?
The solution for 13y^{''}-14y^'+y=0,y(0)=13,y^'(0)= 1/13 is y=-e^t+14e^{t/(13)}