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

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

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

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

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

Solution steps

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

Solve linear ODE:

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

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

y^{^{''}} + 10 y^{^{'}} + 36 y = 0, y (0) = 1, y^{^{'}} (0) = 0

y^{^{''}} + 2 y^{^{'}} - 8 y = 0, y (0) = - 5, y^{^{'}} (0) = 26

(d^{5} - 6 d^{4} + 9 d^{3}) y = 0

y^{^{''}} - 2 y^{^{'}} + 2 y = 0, y (0) = 0, y^{^{'}} (0) = 7

y^{^{'''''}} - 2 y^{^{''''}} + y^{^{'''}} = 0

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