TITLE: E.D.O - Coefficient not constant
QUESTION [0 upvotes]: 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.

REPLY [0 votes]: 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.
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