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

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

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

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

y = (7 - c_{2}) e^{\frac{t}{2}} + c_{2} e^{- 3 t}

Solution steps

2 y^{''} (t) + 5 y^{'} (t) - 3 y = 0

Solve linear ODE:

y = (7 - c_{2}) e^{\frac{t}{2}} + c_{2} e^{- 3 t}

y = (7 - c_{2}) e^{\frac{t}{2}} + c_{2} e^{- 3 t}

3 y^{^{''}} + 12 y^{^{'}} + 24 y = 0

- f^{^{''}} (t) - c f (t) = 0

6 y^{^{''}} - 7 y^{^{'}} + y = 0, y (0) = 6, y^{^{'}} (0) = \frac{1}{6}

y^{^{''}} + 10 y^{^{'}} + 21 y = 0, y (0) = 1, y^{^{'}} (0) = 0

y^{^{''}} + y^{^{'}} + 9.25 y = 0, y^{^{'}} (0) = 8

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