What is the solution for 2y^{''}+5y^'-3y=0,y(0)=-3,y^'(0)=16 ?

The solution for 2y^{''}+5y^'-3y=0,y(0)=-3,y^'(0)=16 is y=2e^{t/2}-5e^{-3t}

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2y^{''}+5y^'-3y=0,y(0)=-3,y^'(0)=16

2 y^{^{''}} + 5 y^{^{'}} - 3 y = 0, y (0) = - 3, y^{^{'}} (0) = 16

y = 2 e^{\frac{t}{2}} - 5 e^{- 3 t}

Solution steps

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

Solve linear ODE:

y = 2 e^{\frac{t}{2}} - 5 e^{- 3 t}

y = 2 e^{\frac{t}{2}} - 5 e^{- 3 t}

y^{^{''}} + 4 y + 68 y = 0, y (0) = 7

3 y^{^{''}} + 48 y = 0, y (0) = 4, y^{^{'}} (0) = 8

y^{^{''''}} + 4 y^{^{'''}} + y^{^{''}} - 4 y^{^{'}} - 2 y = 0

\frac{d ^{2} f}{d x ^{2}} + \frac{df}{d x} = 0

y^{^{''}} + 10 y^{^{'}} + 25 y = 0, y (0) = 0, y^{^{'}} (0) = - 8

What is the solution for 2y^{''}+5y^'-3y=0,y(0)=-3,y^'(0)=16 ?
The solution for 2y^{''}+5y^'-3y=0,y(0)=-3,y^'(0)=16 is y=2e^{t/2}-5e^{-3t}