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

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

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y^{''}+y^'+ky=0

y^{^{''}} + y^{^{'}} + k y = 0

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

Solution steps

y^{''} (t) + y^{'} (t) + k y (t) = 0

Solve linear ODE:

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

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

\frac{d L}{d x}

\frac{d}{d x} (ln (x (x^{2} + 3)^{3}))

\int 10 sec^{2} (x) d x

\frac{d}{d x} ((- 9 x^{2} + 4)^{2})

y = 2 x - x^{2}, y = 0

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