Question

solve the differential equation dy/dx + y cotx =cosx​

Answer 1

Answer:

Comparing the given equation with first order differential equation,

dydx+Py=Q(x), we get, P=cotxandQ(x)=2cosx

So, Integrating factor (I.F)=e∫cotxdx

I.F.=eln|sinx|=sinx

we know, solution of differential equation,

y(I.F.)=∫Q(I.F.)dx

∴Our solution will be,

ysinx=∫sinx(2cosx)dx

⇒ysinx=∫sin2xdx

⇒ysinx=−cos(2x)2+c

At y=0andx=π2, equation becomes

0=−cosπ2+c⇒c=−12

So, solution will be,

ysinx=−cos2x2−12

⇒2ysinx+cos2x+1=0