What is the solution for y^{''}+3y^'+y=0 ?

The solution for y^{''}+3y^'+y=0 is y=c_{1}e^{((-3+sqrt(5))t)/2}+c_{2}e^{((-3-sqrt(5))t)/2}

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y^{''}+3y^'+y=0

y^{^{''}} + 3 y^{^{'}} + y = 0

y = c_{1} e^{\frac{( - 3 + 5 ) t}{2}} + c_{2} e^{\frac{( - 3 - 5 ) t}{2}}

Solution steps

y^{''} (t) + 3 y^{'} (t) + y = 0

Solve linear ODE:

y = c_{1} e^{\frac{( - 3 + 5 ) t}{2}} + c_{2} e^{\frac{( - 3 - 5 ) t}{2}}

y = c_{1} e^{\frac{( - 3 + 5 ) t}{2}} + c_{2} e^{\frac{( - 3 - 5 ) t}{2}}

\int_{2}^{\infty} \frac{1}{e ^{x}} d x

t \to - 2 lim (\frac{t + 2}{t ^{2} - 4})

x \frac{d y}{d x} + 10 y = 9 y^{2}, y (1) = - 1

\frac{d y}{d x} + 4 x^{2} y = - 10 x^{2}

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

What is the solution for y^{''}+3y^'+y=0 ?
The solution for y^{''}+3y^'+y=0 is y=c_{1}e^{((-3+sqrt(5))t)/2}+c_{2}e^{((-3-sqrt(5))t)/2}