en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

8(d^2y)/(dt^2)+12(dy)/(dt)+5y=0

Solution

8 \frac{d ^{2} y}{d t ^{2}} + 12 \frac{d y}{d t} + 5 y = 0

Solution

y = e^{- \frac{3 t}{4}} (c_{1} cos (\frac{t}{4}) + c_{2} sin (\frac{t}{4}))

Solution steps

8 \frac{d ^{2} y}{d t ^{2}} + 12 \frac{d y}{d t} + 5 y = 0

Solve linear ODE:

y = e^{- \frac{3 t}{4}} (c_{1} cos (\frac{t}{4}) + c_{2} sin (\frac{t}{4}))

y = e^{- \frac{3 t}{4}} (c_{1} cos (\frac{t}{4}) + c_{2} sin (\frac{t}{4}))

Graph

Popular Examples

(d^2y)/(dt^2)-18(dy)/(dt)+81y=0

\frac{d ^{2} y}{d t ^{2}} - 18 \frac{d y}{d t} + 81 y = 0

y^{'''}+4y^{''}-25y^'-28y=0

y^{^{'''}} + 4 y^{^{''}} - 25 y^{^{'}} - 28 y = 0

y^{''}+3y^'+6*y=0,y(0)=0,y^'(0)=1

y^{^{''}} + 3 y^{^{'}} + 6 \cdot y = 0, y (0) = 0, y^{^{'}} (0) = 1

y^{''}-4y^'+4y=0,y(0)=8.1,y^'(0)=3.9

y^{^{''}} - 4 y^{^{'}} + 4 y = 0, y (0) = 8.1, y^{^{'}} (0) = 3.9

y^{'''}+y^{''}-24y^'+36y=0

y^{^{'''}} + y^{^{''}} - 24 y^{^{'}} + 36 y = 0

Frequently Asked Questions (FAQ)

What is the solution for 8(d^2y)/(dt^2)+12(dy)/(dt)+5y=0 ?
The solution for 8(d^2y)/(dt^2)+12(dy)/(dt)+5y=0 is y=e^{-(3t)/4}(c_{1}cos(t/4)+c_{2}sin(t/4))