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

The solution for -y^{''}+y^'+y=0 is y=c_{1}e^{-((-1+sqrt(5))t)/2}+c_{2}e^{((1+sqrt(5))t)/2}

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

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

y = c_{1} e^{- \frac{( - 1 + 5 ) t}{2}} + c_{2} e^{\frac{( 1 + 5 ) t}{2}}

Solution steps

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

Solve linear ODE:

y = c_{1} e^{- \frac{( - 1 + 5 ) t}{2}} + c_{2} e^{\frac{( 1 + 5 ) t}{2}}

y = c_{1} e^{- \frac{( - 1 + 5 ) t}{2}} + c_{2} e^{\frac{( 1 + 5 ) t}{2}}

\frac{d}{d x} (\frac{x ^{2} - 3 x + 2}{2 x ^{2} + 5 x - 1})

\frac{\partial}{\partial y} (\frac{2 y}{x + y ^{2}})

\int \frac{5 ln ^{2} ( x ) + 9}{x} d x

\frac{\partial}{\partial x} (y^{2} + x y + 3 y + 2 x + 3)

\int \frac{1}{5 sin ( x ) + 3} d x

What is the solution for -y^{''}+y^'+y=0 ?
The solution for -y^{''}+y^'+y=0 is y=c_{1}e^{-((-1+sqrt(5))t)/2}+c_{2}e^{((1+sqrt(5))t)/2}