Find the solution of the differential equation #xy'=y+x^2\sinx# that satisfies the given initial conditions below?

Question

#y(\pi)=0#

I know it's in #dy/dx+P(x)y=Q(x)# form, but what exactly is the integrating factor?

Like what is "exp" in #I=exp(\int P(x)dx)#?
(People use this a lot when mentioning the integrating factor, but I learned it as #I(x)=e^(\intP(x)dx)#...)

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Answer 1 · 2018-04-25T06:51:30

Refer to the Explanation.

#exp# in #exp(intP(x)dx)# means exponential function.

So, #exp(intP(x)dx)# is just another way to denote

#e^(intP(x)dx)#.

I hope I've cleared your doubt!

By the way, I presume that you know how to solve the given diff.

eqn., so, I don't solve it!