What is the solution for 2y^{''}+5y^'-3y=0,y(0)=-1,y^'(0)=17 ?

The solution for 2y^{''}+5y^'-3y=0,y(0)=-1,y^'(0)=17 is y=4e^{t/2}-5e^{-3t}

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2y^{''}+5y^'-3y=0,y(0)=-1,y^'(0)=17

2 y^{^{''}} + 5 y^{^{'}} - 3 y = 0, y (0) = - 1, y^{^{'}} (0) = 17

y = 4 e^{\frac{t}{2}} - 5 e^{- 3 t}

Solution steps

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

Solve linear ODE:

y = 4 e^{\frac{t}{2}} - 5 e^{- 3 t}

y = 4 e^{\frac{t}{2}} - 5 e^{- 3 t}

y^{^{'''}} - 3 y^{^{''}} - 25 y^{^{'}} - 21 y = 0

0.5 y^{^{''}} + 6 y^{^{'}} + 50 y = 0

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

\frac{d ^{3} y}{d x ^{3}} = \frac{d y}{d x}

16 y^{^{''''}} = 625 y

What is the solution for 2y^{''}+5y^'-3y=0,y(0)=-1,y^'(0)=17 ?
The solution for 2y^{''}+5y^'-3y=0,y(0)=-1,y^'(0)=17 is y=4e^{t/2}-5e^{-3t}