What is the solution for 5y^{''}-2y^'-7y=0,y(0)=3,y^'(0)=9 ?

The solution for 5y^{''}-2y^'-7y=0,y(0)=3,y^'(0)=9 is y=5e^{(7t)/5}-2e^{-t}

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5y^{''}-2y^'-7y=0,y(0)=3,y^'(0)=9

5 y^{^{''}} - 2 y^{^{'}} - 7 y = 0, y (0) = 3, y^{^{'}} (0) = 9

y = 5 e^{\frac{7 t}{5}} - 2 e^{- t}

Solution steps

5 y^{''} (t) - 2 y^{'} (t) - 7 y = 0

Solve linear ODE:

y = 5 e^{\frac{7 t}{5}} - 2 e^{- t}

y = 5 e^{\frac{7 t}{5}} - 2 e^{- t}

y^{^{''}} - 6 y + 9 y = 0, y^{1} (0) = e^{3 x}

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

y^{^{''}} - 3 y^{^{'}} + 2 y = 0, y (0) = 1, y^{^{'}} (0) = 1

y^{^{''}} - 4 y^{^{'}} + 11 y = 0

\frac{y ^{^{''}}}{y ^{^{'}}} = 1

What is the solution for 5y^{''}-2y^'-7y=0,y(0)=3,y^'(0)=9 ?
The solution for 5y^{''}-2y^'-7y=0,y(0)=3,y^'(0)=9 is y=5e^{(7t)/5}-2e^{-t}