Solve the following differential equation dy dx x y 1 2 if y 0 0 ........

Explanation:

dy/dx  =(x+y+1)²  

putting x+y+1 =t

taking differentiation

dy/dx   =dt/dx  -1

given equation becomes  dt/dx -1  =t²

dt/dx  =t²  +1

? dt/t² +1  = ? dx

tan^-1  t  =x+c

 x+y+1  =tan (x+c)

x=0 ,y=0

tan c=1

c=π/4

x+y+1 =tan(x+ π/4)