What is the solution for 2y^{''}-7y^'-15y=0,y(0)=2,y^'(0)=1 ?

The solution for 2y^{''}-7y^'-15y=0,y(0)=2,y^'(0)=1 is y=(2-18/13)e^{5t}+18/13 e^{-(3t)/2}

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2y^{''}-7y^'-15y=0,y(0)=2,y^'(0)=1

2 y^{^{''}} - 7 y^{^{'}} - 15 y = 0, y (0) = 2, y^{^{'}} (0) = 1

y = (2 - \frac{18}{13}) e^{5 t} + \frac{18}{13} e^{- \frac{3 t}{2}}

Solution steps

2 y^{''} (t) - 7 y^{'} (t) - 15 y = 0

Solve linear ODE:

y = (2 - \frac{18}{13}) e^{5 t} + \frac{18}{13} e^{- \frac{3 t}{2}}

y = (2 - \frac{18}{13}) e^{5 t} + \frac{18}{13} e^{- \frac{3 t}{2}}

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What is the solution for 2y^{''}-7y^'-15y=0,y(0)=2,y^'(0)=1 ?
The solution for 2y^{''}-7y^'-15y=0,y(0)=2,y^'(0)=1 is y=(2-18/13)e^{5t}+18/13 e^{-(3t)/2}