What is the solution for y^'+y=sin(t) ?

The solution for y^'+y=sin(t) is y=-(cos(t))/2+(sin(t))/2+(c_{1})/(e^t)

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y^'+y=sin(t)

y^{^{'}} + y = sin (t)

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

Solution steps

y^{'} (t) + y = sin (t)

Solve linear ODE:

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

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

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