What is the solution for y^{''}-7y^'+10y=0,y(0)=1,y^'(0)=8 ?

The solution for y^{''}-7y^'+10y=0,y(0)=1,y^'(0)=8 is y=2e^{5t}-e^{2t}

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y^{''}-7y^'+10y=0,y(0)=1,y^'(0)=8

y^{^{''}} - 7 y^{^{'}} + 10 y = 0, y (0) = 1, y^{^{'}} (0) = 8

y = 2 e^{5 t} - e^{2 t}

Solution steps

y^{''} (t) - 7 y^{'} (t) + 10 y = 0

Solve linear ODE:

y = 2 e^{5 t} - e^{2 t}

y = 2 e^{5 t} - e^{2 t}

y^{^{'''}} - 3 y^{^{''}} + 9 y^{^{'}} + 13 y = 0

y^{^{''}} + 2 y^{^{'}} + 2 y = 0, y (\frac{π}{2}) = 0, y^{^{'}} (\frac{π}{2}) = 3

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

y^{^{''}} - 3 y^{^{'}} + (2 + a) y = 0

y^{^{''}} - 11 y^{^{'}} = 0

What is the solution for y^{''}-7y^'+10y=0,y(0)=1,y^'(0)=8 ?
The solution for y^{''}-7y^'+10y=0,y(0)=1,y^'(0)=8 is y=2e^{5t}-e^{2t}