What is the solution for 2y^{''}+5y^'-3y=0,y(0)=5,y^{''}(0)=13 ?

The solution for 2y^{''}+5y^'-3y=0,y(0)=5,y^{''}(0)=13 is y=(5-47/35)e^{t/2}+47/35 e^{-3t}

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2y^{''}+5y^'-3y=0,y(0)=5,y^{''}(0)=13

2 y^{^{''}} + 5 y^{^{'}} - 3 y = 0, y (0) = 5, y^{^{''}} (0) = 13

y = (5 - \frac{47}{35}) e^{\frac{t}{2}} + \frac{47}{35} e^{- 3 t}

Solution steps

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

Solve linear ODE:

y = (5 - \frac{47}{35}) e^{\frac{t}{2}} + \frac{47}{35} e^{- 3 t}

y = (5 - \frac{47}{35}) e^{\frac{t}{2}} + \frac{47}{35} e^{- 3 t}

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

\frac{d ^{2} y}{d x ^{2}} + \frac{d y}{d x} + 5 y = 0

x^{^{''}} + c x = 0

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

\frac{d ^{2} y}{d x ^{2}} + 6 \frac{d y}{d x} + 10 y = 0

What is the solution for 2y^{''}+5y^'-3y=0,y(0)=5,y^{''}(0)=13 ?
The solution for 2y^{''}+5y^'-3y=0,y(0)=5,y^{''}(0)=13 is y=(5-47/35)e^{t/2}+47/35 e^{-3t}