Hello Guys i've been being difficulty to solve this Differential equation, because the coefficients aren't constant. I don't have an idea to solve.
$\frac{dx}{dt}*sin(t) + x*\cos(t) = 1 , (t,x) \in (0,\pi)\times\mathbb{R}$
I'd like to find a general solution.
Thanks.
Note that $$\frac{dx}{dt}*sin(t) + x*\cos(t) = \frac {d}{dt} ( x\sin t ) $$
Thus you have $$\frac {d}{dt} ( x\sin t )=1 $$
Upon integrating you get
$$ x \sin t = t+c $$
Solve for x and find your constant from initial conditions.