What is the solution for y^{''}=ky(x) ?

The solution for y^{''}=ky(x) is y=c_{1}e^{sqrt(k)x}+c_{2}e^{-sqrt(k)x}

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

y^{''}=ky(x)

y^{^{''}} = k y (x)

y = c_{1} e^{k x} + c_{2} e^{- k x}

Solution steps

y^{''} (x) = k y (x)

Solve linear ODE:

y = c_{1} e^{k x} + c_{2} e^{- k x}

y = c_{1} e^{k x} + c_{2} e^{- k x}

4 \frac{d ^{2} x}{d t ^{2}} + c \frac{d x}{d t} + k (x) = 0

\frac{d ^{2} y}{d x ^{2}} - 10 \frac{d y}{d x} + 34 y = 0

y^{^{''}} + 10 y^{^{'}} + 25 y = 0, y (0) = - 4, y^{^{'}} (0) = 18

6 y^{^{''}} + 108 y^{^{'}} + 486 y = 0

y^{^{''}} - 6 y^{^{'}} + 8 y = 0, y (0) = \frac{3}{2}, y^{^{'}} (0) = \frac{5}{2}

What is the solution for y^{''}=ky(x) ?
The solution for y^{''}=ky(x) is y=c_{1}e^{sqrt(k)x}+c_{2}e^{-sqrt(k)x}