Find the particular solution of the differential equation e^x √(1-y^2)dx + y/x dx = 0

Question

Find the particular solution of the differential equation \(e^x\sqrt{1-y^2}dx+\frac yxdy=0\) given that y = 1 when x = 0
 

Answer 1

 We have,

(Using ILATE on LHS)

Therefore, required particular solution is \(xe^x-e^x=\sqrt{1-y^2}-1\)