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)

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(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}}

\frac{1}{2} x

\frac{d}{d x} (\frac{18 x + 2 x ^{2}}{( 9 + 2 x ) ^{2}})

\int \frac{1}{( 49 + x ^{2} ) ^{\frac{3}{2}}} d x

\int_{- 1}^{3} (x^{2} - 4 x + 3) d x

\int sin^{2} (2 x) cos^{2} (2 x) d x

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)