en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

y^{''}-5y^'-14y=0,y(0)=α,y^'(0)=-14

Solution

y^{^{''}} - 5 y^{^{'}} - 14 y = 0, y (0) = α, y^{^{'}} (0) = - 14

Solution

y = e^{7 t} (α + \frac{- 14 - 7 α}{9}) - \frac{e ^{- 2 t} ( - 14 - 7 α )}{9}

Solution steps

y^{''} (t) - 5 y^{'} (t) - 14 y = 0

Solve linear ODE:

y = e^{7 t} (α + \frac{- 14 - 7 α}{9}) - \frac{e ^{- 2 t} ( - 14 - 7 α )}{9}

y = e^{7 t} (α + \frac{- 14 - 7 α}{9}) - \frac{e ^{- 2 t} ( - 14 - 7 α )}{9}

Graph

Popular Examples

(d^2x)/(dt^2)+12(dx)/(dt)+32x=0

\frac{d ^{2} x}{d t ^{2}} + 12 \frac{d x}{d t} + 32 x = 0

y^{^{'''}} - 16 y = 0

y^{''}+a*y^'+b*y=0

y^{^{''}} + a \cdot y^{^{'}} + b \cdot y = 0

(3440.3669700000000…)y^{''}+(0)y^'+(22500)y=0

(3440.3669700000000 \dots) y^{^{''}} + (0) y^{^{'}} + (22500) y = 0

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

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

Frequently Asked Questions (FAQ)

What is the solution for y^{''}-5y^'-14y=0,y(0)=α,y^'(0)=-14 ?
The solution for y^{''}-5y^'-14y=0,y(0)=α,y^'(0)=-14 is y=e^{7t}(α+(-14-7α)/9)-(e^{-2t}(-14-7α))/9