What is the solution for 2y^{''}+5y^'-3y=0,y(0)=-1,y^'(0)=10 ?

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

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2y^{''}+5y^'-3y=0,y(0)=-1,y^'(0)=10

2 y^{^{''}} + 5 y^{^{'}} - 3 y = 0, y (0) = - 1, y^{^{'}} (0) = 10

y = 2 e^{\frac{t}{2}} - 3 e^{- 3 t}

Solution steps

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

Solve linear ODE:

y = 2 e^{\frac{t}{2}} - 3 e^{- 3 t}

y = 2 e^{\frac{t}{2}} - 3 e^{- 3 t}

4 y^{^{''}} - 3 y^{^{'}} - y = 0

4 y^{^{''}} + 324 y = 0

y^{^{''}} - 6 y^{^{'}} + 25 y = 0, y (0) = 6, y^{^{'}} (0) = - 2

y^{^{''}} - 5 y^{^{'}} - 36 y = 0, y (0) = - 2, y^{^{'}} (0) = 3

y^{^{''}} + 12 y^{^{'}} + 36 y = 0, y (0) = - 5, y^{^{'}} (0) = 33

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