What is the solution for 2y^{''}+y^'-4y=0 ?

The solution for 2y^{''}+y^'-4y=0 is y=c_{1}e^{((-1+sqrt(33))t)/4}+c_{2}e^{((-1-sqrt(33))t)/4}

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2y^{''}+y^'-4y=0

2 y^{^{''}} + y^{^{'}} - 4 y = 0

y = c_{1} e^{\frac{( - 1 + 33 ) t}{4}} + c_{2} e^{\frac{( - 1 - 33 ) t}{4}}

Solution steps

2 y^{''} (t) + y^{'} (t) - 4 y = 0

Solve linear ODE:

y = c_{1} e^{\frac{( - 1 + 33 ) t}{4}} + c_{2} e^{\frac{( - 1 - 33 ) t}{4}}

y = c_{1} e^{\frac{( - 1 + 33 ) t}{4}} + c_{2} e^{\frac{( - 1 - 33 ) t}{4}}

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What is the solution for 2y^{''}+y^'-4y=0 ?
The solution for 2y^{''}+y^'-4y=0 is y=c_{1}e^{((-1+sqrt(33))t)/4}+c_{2}e^{((-1-sqrt(33))t)/4}