xy'-y=tan(y/x)
Book says y=x[arcsin(cx+2npi)] or y=x[-arcsin(cx+(2n-1)pi)], & y=0
I get y=0 (easy)

but when i solve i get y=x[arcsin(ce^-(1/x)+2npi)]

Question

xy'-y=tan(y/x)
Book says y=x[arcsin(cx+2npi)] or y=x[-arcsin(cx+(2n-1)pi)], & y=0
I get y=0 (easy)

but when i solve i get y=x[arcsin(ce^-(1/x)+2npi)]

anonymous · Answer

i also understand the shift of equation as a result of the integral of $$\int\limits_{}^{}\cot (v)= \ln \left| \sin(v) \right|$$
the positive value y=x[arcsin(cx+2npi)] negative value y=x[-arcsin(cx+(2n-1)pi)]

turingtest · Answer

you are in good company, wolfram has your answer http://www.wolframalpha.com/input/?i=xy%27-y%3Dtan%28y%2Fx%29 not sure if that's somehow the same as the books answer, but I don't see how...