The solution of the differential equation dydx=xy+x+y+1 is
y=12x2+x+c
logy+1=12x2+x+c
cy+1=ex2+x
None of these.
Explanation of the correct option.
Compute the required value.
Given : dydx=xy+x+y+1
⇒ dydx=x(y+1)+y+1
⇒ dydx=(x+1)(y+1)
⇒ dyy+1=(x+1)dx
Now, Integrate both side,
⇒logy+1=x22+x+c ∫1x+adx=logx+a,∫xndx=xn+1
Hence option B is the correct option.
The solution of the differential equation dydx=1+x+y+xy is