What is the solution for 6y^{''}+y^'-y=0 ?

The solution for 6y^{''}+y^'-y=0 is y=c_{1}e^{t/3}+c_{2}e^{-t/2}

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6y^{''}+y^'-y=0

6 y^{^{''}} + y^{^{'}} - y = 0

y = c_{1} e^{\frac{t}{3}} + c_{2} e^{- \frac{t}{2}}

Solution steps

6 y^{''} (t) + y^{'} (t) - y = 0

Solve linear ODE:

y = c_{1} e^{\frac{t}{3}} + c_{2} e^{- \frac{t}{2}}

y = c_{1} e^{\frac{t}{3}} + c_{2} e^{- \frac{t}{2}}

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\frac{d}{d x} (2 - e^{x})

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What is the solution for 6y^{''}+y^'-y=0 ?
The solution for 6y^{''}+y^'-y=0 is y=c_{1}e^{t/3}+c_{2}e^{-t/2}