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

The solution for 2y^{''}-y^'-2y=0 is y=c_{1}e^{((1+sqrt(17))t)/4}+c_{2}e^{((1-sqrt(17))t)/4}

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

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

y = c_{1} e^{\frac{( 1 + 17 ) t}{4}} + c_{2} e^{\frac{( 1 - 17 ) t}{4}}

Solution steps

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

Solve linear ODE:

y = c_{1} e^{\frac{( 1 + 17 ) t}{4}} + c_{2} e^{\frac{( 1 - 17 ) t}{4}}

y = c_{1} e^{\frac{( 1 + 17 ) t}{4}} + c_{2} e^{\frac{( 1 - 17 ) t}{4}}

a y^{^{''}} + b y^{^{'}} + cy = 0, y (0) = 0

y^{^{''}} - 10 y^{^{'}} + 41 y = 0, y (0) = 10, y^{^{'}} (0) = 7

(d^{3} + 6 d^{2} + 11 d + 6) y = 0

y^{^{''}} + 3 y^{^{'}} - 10 y = 0, y (0) = 1, y^{^{'}} (0) = - 3

y^{^{''}} + 10 y^{^{'}} + 36 y = 0, y (0) = 1, y^{^{'}} (0) = 0

What is the solution for 2y^{''}-y^'-2y=0 ?
The solution for 2y^{''}-y^'-2y=0 is y=c_{1}e^{((1+sqrt(17))t)/4}+c_{2}e^{((1-sqrt(17))t)/4}