What is the solution for y^{''}-3y^'-10y=0,y(0)=1,y^'(0)=10 ?

The solution for y^{''}-3y^'-10y=0,y(0)=1,y^'(0)=10 is y=(1+5/7)e^{5t}-5/7 e^{-2t}

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y^{''}-3y^'-10y=0,y(0)=1,y^'(0)=10

y^{^{''}} - 3 y^{^{'}} - 10 y = 0, y (0) = 1, y^{^{'}} (0) = 10

y = (1 + \frac{5}{7}) e^{5 t} - \frac{5}{7} e^{- 2 t}

Solution steps

y^{''} (t) - 3 y^{'} (t) - 10 y = 0

Solve linear ODE:

y = (1 + \frac{5}{7}) e^{5 t} - \frac{5}{7} e^{- 2 t}

y = (1 + \frac{5}{7}) e^{5 t} - \frac{5}{7} e^{- 2 t}

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What is the solution for y^{''}-3y^'-10y=0,y(0)=1,y^'(0)=10 ?
The solution for y^{''}-3y^'-10y=0,y(0)=1,y^'(0)=10 is y=(1+5/7)e^{5t}-5/7 e^{-2t}