Question

find general solution of dy/dx=x(2logx+1)/siny+ycosy

Answer 1

hey i think u miss the value if y=90
dy​/dx=x(2logx+1)/(siny+ycosy)
Separating terms of y and x,
(siny+ycosy)dy=(2xlogx+x)dx
Integrating both sides,
-cosy+ysiny+cosy = 2x​2logx/2 - 2x2/4 + x2/2 + c ysiny=x2logx  -  x2/2  +  x2/2  +  c
ysiny=x2logx + c
NOW putting x=1 and y=90o or π/2
we get, c=π/2
so the particular DIFFERENTIAL EQUATION =
ysiny=x2logx+π/2