What is the solution for 2y^{''}+5y^'-3y=0,y(0)=-5,y^'(0)=22 ?

The solution for 2y^{''}+5y^'-3y=0,y(0)=-5,y^'(0)=22 is y=2e^{t/2}-7e^{-3t}

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2y^{''}+5y^'-3y=0,y(0)=-5,y^'(0)=22

2 y^{^{''}} + 5 y^{^{'}} - 3 y = 0, y (0) = - 5, y^{^{'}} (0) = 22

y = 2 e^{\frac{t}{2}} - 7 e^{- 3 t}

Solution steps

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

Solve linear ODE:

y = 2 e^{\frac{t}{2}} - 7 e^{- 3 t}

y = 2 e^{\frac{t}{2}} - 7 e^{- 3 t}

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

2 y^{^{''}} + 5 y^{^{'}} - 3 y = 0, y (0) = - 5, y^{^{'}} (0) = 29

2 x^{^{''}} + 3 x^{^{'}} - 2 x = 0

(d^{4} - 6 d^{3} - 12 d^{2} + 38 d - 21) y = 0

20 y^{^{''}} + 80 y^{^{'}} + 60 y = 0

What is the solution for 2y^{''}+5y^'-3y=0,y(0)=-5,y^'(0)=22 ?
The solution for 2y^{''}+5y^'-3y=0,y(0)=-5,y^'(0)=22 is y=2e^{t/2}-7e^{-3t}