What is the solution for 1296y^{''}+72y^'+y=0,y(0)=7,y^'(0)=5 ?

The solution for 1296y^{''}+72y^'+y=0,y(0)=7,y^'(0)=5 is y=7e^{-t/(36)}+(187e^{-t/(36)}t)/(36)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

1296y^{''}+72y^'+y=0,y(0)=7,y^'(0)=5

1296 y^{^{''}} + 72 y^{^{'}} + y = 0, y (0) = 7, y^{^{'}} (0) = 5

y = 7 e^{- \frac{t}{36}} + \frac{187 e ^{- \frac{t}{36}} t}{36}

Solution steps

1296 y^{''} (t) + 72 y^{'} (t) + y = 0

Solve linear ODE:

y = 7 e^{- \frac{t}{36}} + \frac{187 e ^{- \frac{t}{36}} t}{36}

y = 7 e^{- \frac{t}{36}} + \frac{187 e ^{- \frac{t}{36}} t}{36}

y^{^{''}} - 16 y = 0, y (0) = 13, y^{^{'}} (0) = 20

y^{^{''}} + 6 y^{^{'}} + 5 y = 0, y (0) = 0, y^{^{'}} (0) = 0

2 y^{^{'''}} + 7 y^{^{''}} - 17 y^{^{'}} - 10 y = 0

1 y^{^{''}} + 3 y^{^{'}} + 2 y = 0

2 y^{^{''''}} + 4 y^{^{''}} + 2 y = 0

What is the solution for 1296y^{''}+72y^'+y=0,y(0)=7,y^'(0)=5 ?
The solution for 1296y^{''}+72y^'+y=0,y(0)=7,y^'(0)=5 is y=7e^{-t/(36)}+(187e^{-t/(36)}t)/(36)