What is the solution for y^{''}-5y^'+5y=0 ?

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

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y^{''}-5y^'+5y=0

y^{^{''}} - 5 y^{^{'}} + 5 y = 0

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

Solution steps

y^{''} (t) - 5 y^{'} (t) + 5 y = 0

Solve linear ODE:

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

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

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

\frac{d}{d x} (cos ((8 x^{2} + 9)^{5}))

f (x) g (x)

2 x^{2} + x - 1

x \to - 6 lim (\frac{( x ^{2} - 36 )}{x + 6})

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