What is the solution for y+6y^'+13y=10,e^{2t}y=-13 ?

The solution for y+6y^'+13y=10,e^{2t}y=-13 is y=-(e^{(-7t-c_{1})/3})/(7)+5/7

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y+6y^'+13y=10,e^{2t}y=-13

y + 6 y^{^{'}} + 13 y = 10, e^{2 t} y = - 13

y = - \frac{e ^{\frac{- 7 t - c _{1}}{3}}}{7} + \frac{5}{7}

Solution steps

y + 6 y^{'} (t) + 13 y = 10

Solve separable ODE:

y = - \frac{e ^{\frac{- 7 t - c _{1}}{3}}}{7} + \frac{5}{7}

y = - \frac{e ^{\frac{- 7 t - c _{1}}{3}}}{7} + \frac{5}{7}

\frac{d y}{d t} = 5 - \frac{7}{400} y

\frac{d y}{d x} = 3 x^{2} (y^{2} + 4)

\frac{df}{d t} = - 0.01 \cdot f (t)^{(1.84)}

x^{2} sin (y) d x - cot (y) d y = 0

\frac{d x}{d t} = 0.09 - \frac{x}{2580}

What is the solution for y+6y^'+13y=10,e^{2t}y=-13 ?
The solution for y+6y^'+13y=10,e^{2t}y=-13 is y=-(e^{(-7t-c_{1})/3})/(7)+5/7