Solve:

dy/dx = 1 + x + y + xy

Answer given in the book is : log | 1 + y| = x + 1/2 x² + C

Question

Solve:
dy/dx = 1 + x + y + xy
Answer given in the book is : log | 1 + y| = x + 1/2
x2 + C

Vipin Verma · Accepted Answer

dydx = 1+x+y +xy⇒ dydx = (1+x)(1+y)⇒ dy1+y=(1+x)dx
[variable seperable]Integrating both sides, we get∫ dy1+y =
∫(1+x)dx⇒ ln|1+y| =x+x22 +C

Solve: dy/dx = 1 + x + y + xy Answer given in the book is : log | 1 + y| = x + 1/2 x2 + C