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

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

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

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

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

Solution steps

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

Solve linear ODE:

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

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

y^{^{''''}} - 36 y^{^{'''}} + 324 y^{^{''}} = 0

x^{^{''}} + 9 x = 0, x (0) = 3, x^{^{'}} (0) = 4

y^{^{''}} - 7 y^{^{'}} + 2 y = 0

\frac{d ^{2} y}{d t ^{2}} + 7 \frac{d y}{d t} + k y = 0

y^{^{''}} - 4 y^{^{'}} + 5 y = 0, y (0) = - 1, y^{^{'}} (0) = 5

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