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

Daniaal Sanchez

Daniaal Sanchez

Answered question

2021-02-13

Find the solution (xsinyx)dy=(ysinyxx)dx

Answer & Explanation

ensojadasH

ensojadasH

Skilled2021-02-14Added 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)

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