Find the solution (xsiny/x)dy=(ysiny/x -x)dx

Daniaal Sanchez 2021-02-13 Answered
Find the solution (xsinyx)dy=(ysinyxx)dx
You can still ask an expert for help

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

Solve your problem for the price of one coffee

  • Available 24/7
  • Math expert for every subject
  • Pay only if we can solve it
Ask Question

Expert Answer

ensojadasH
Answered 2021-02-14 Author has 100 answers
The DE is x. sin(yx)dy=(y.sin(yx)x)dx, giving
dydx=yx1sin(yx)
let v=yx, then y=vxanddydx=v+x.dvdx
Substituting for v and dydx into the DE,
v+x.dvdx=v1sin(v)
x.dvdx=1sin(v)
sin(v)dv=(1x)dx
integrating both sides,
cos(v)=ln(x)+K
cos(yx)=ln(x)+K
y=x.acos(ln(x)+K)
Not exactly what you’re looking for?
Ask My Question

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more