What is the solution for y^{''}-5y^'-6y=10,y(0)=2,y^'(0)=1 ?

The solution for y^{''}-5y^'-6y=10,y(0)=2,y^'(0)=1 is y=(-3+11/3)e^{6t}+3e^{-t}-5/3

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y^{''}-5y^'-6y=10,y(0)=2,y^'(0)=1

y^{^{''}} - 5 y^{^{'}} - 6 y = 10, y (0) = 2, y^{^{'}} (0) = 1

y = (- 3 + \frac{11}{3}) e^{6 t} + 3 e^{- t} - \frac{5}{3}

Solution steps

y^{''} (t) - 5 y^{'} (t) - 6 y = 10

Solve linear ODE:

y = (- 3 + \frac{11}{3}) e^{6 t} + 3 e^{- t} - \frac{5}{3}

y = (- 3 + \frac{11}{3}) e^{6 t} + 3 e^{- t} - \frac{5}{3}

What is the solution for y^{''}-5y^'-6y=10,y(0)=2,y^'(0)=1 ?
The solution for y^{''}-5y^'-6y=10,y(0)=2,y^'(0)=1 is y=(-3+11/3)e^{6t}+3e^{-t}-5/3