The solution of cosy+(xsiny-1)dydx=0
xsecy=tany+C
tany–secy=Cx
tany+secy=Cx
xsecy+tany=C
Find the solution of the given expression
Given: cosy+(xsiny-1)dydx=0
⇒cosycosy+(xsiny-1)cosydydx=0cosy⇒1+(xsiny-1)cosydydx=0⇒xsinycosy-1cosydydx=-1⇒xsinycosy-1cosy=-dxdy
⇒dxdy+xsinycosy-1cosy=0
⇒dxdy+tanyx=secy , linear in x
So, I.F.=e∫tanydy
=e∫sinycosydy=elnsecy=secy
Therefore, solution is xsecy=∫sec2ydy+C
Hence, option (A) is the correct answer.