What is the solution for (dy)/(dt)+y=cos(t),y(0)=1 ?

The solution for (dy)/(dt)+y=cos(t),y(0)=1 is y=(sin(t))/2+(cos(t))/2+1/(2e^t)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

(dy)/(dt)+y=cos(t),y(0)=1

\frac{d y}{d t} + y = cos (t), y (0) = 1

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

Solution steps

\frac{d y}{d t} + y = cos (t)

Solve linear ODE:

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

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

What is the solution for (dy)/(dt)+y=cos(t),y(0)=1 ?
The solution for (dy)/(dt)+y=cos(t),y(0)=1 is y=(sin(t))/2+(cos(t))/2+1/(2e^t)