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

The solution for y^{''}-5y^'+y=0 is y=c_{1}e^{((5+sqrt(21))t)/2}+c_{2}e^{((5-sqrt(21))t)/2}

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

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

y = c_{1} e^{\frac{( 5 + 21 ) t}{2}} + c_{2} e^{\frac{( 5 - 21 ) t}{2}}

Solution steps

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

Solve linear ODE:

y = c_{1} e^{\frac{( 5 + 21 ) t}{2}} + c_{2} e^{\frac{( 5 - 21 ) t}{2}}

y = c_{1} e^{\frac{( 5 + 21 ) t}{2}} + c_{2} e^{\frac{( 5 - 21 ) t}{2}}

\frac{d ^{2} x}{d t ^{2}} + 4 x = 0

x^{^{''}} + 16 x = 0, x (0) = 0, x^{^{'}} (0) = 5

y^{^{''}} + 12 y^{^{'}} + 36 y = 0, y (0) = 3, y^{^{'}} (0) = 0

y^{^{''''}} - 42 y^{^{'''}} + 441 y^{^{''}} = 0

{\frac{d ^{2} y}{d x ^{2}} + 4 \frac{d y}{d x} + 20 y}^{2} = 0

What is the solution for y^{''}-5y^'+y=0 ?
The solution for y^{''}-5y^'+y=0 is y=c_{1}e^{((5+sqrt(21))t)/2}+c_{2}e^{((5-sqrt(21))t)/2}