en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

y^{''}+7y^'+6y=3sin(2t)

Solution

y^{^{''}} + 7 y^{^{'}} + 6 y = 3 sin (2 t)

Solution

y = c_{1} e^{- t} + c_{2} e^{- 6 t} + \frac{3}{100} sin (2 t) - \frac{21}{100} cos (2 t)

Solution steps

y^{''} (t) + 7 y^{'} (t) + 6 y = 3 sin (2 t)

Solve linear ODE:

y = c_{1} e^{- t} + c_{2} e^{- 6 t} + \frac{3}{100} sin (2 t) - \frac{21}{100} cos (2 t)

y = c_{1} e^{- t} + c_{2} e^{- 6 t} + \frac{3}{100} sin (2 t) - \frac{21}{100} cos (2 t)

Graph

Popular Examples

y^{''}-2y^'+5y=2x^2+12

y^{^{''}} - 2 y^{^{'}} + 5 y = 2 x^{2} + 12

y^{''}+2y^'+y=5e^{-t}

y^{^{''}} + 2 y^{^{'}} + y = 5 e^{- t}

y^{''}+y=-cos(2t),y(0)=0,y^'(0)=0

y^{^{''}} + y = - cos (2 t), y (0) = 0, y^{^{'}} (0) = 0

y^{''}+2y^'+5y=50xsin(x)+100xcos(x)

y^{^{''}} + 2 y^{^{'}} + 5 y = 50 x sin (x) + 100 x cos (x)

y^{''}-4y=-7e^{2x}+x,y(0)=1,y^'(0)=3

y^{^{''}} - 4 y = - 7 e^{2 x} + x, y (0) = 1, y^{^{'}} (0) = 3

Frequently Asked Questions (FAQ)

What is the solution for y^{''}+7y^'+6y=3sin(2t) ?
The solution for y^{''}+7y^'+6y=3sin(2t) is y=c_{1}e^{-t}+c_{2}e^{-6t}+3/100 sin(2t)-21/100 cos(2t)