For the sulotion of the OED: \frac{dy}{dx}=1+x+y^{2}+xy.

Priscilla Johnston 2022-01-19 Answered
For the sulotion of the OED: dydx=1+x+y2+xy.
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yotaniwc
Answered 2022-01-19 Author has 34 answers
Changing y=uz2 the equation is cast to the form
dudx=u2+(x21)2+52
which does not seem to possess solutions in terms of elementary functions
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limacarp4
Answered 2022-01-20 Author has 39 answers
if we know yp=x22x1x24x+3 is a particular solution. So we can find general solution of Riccati Equation. (Note:I did not try it .I trust GEdgar. Thanks to him. I just offer a general solution If we know a particular solution)
Use transform of y=yp+1H
dydx=1+x+y2+xy.
yp+(HH2)=1+x+(yp2+2ypH+1H2)+xyp+xH
yp=1+x+yp2+xyp+HH2+2ypH+1H2+xH
if yp is a solution of the equation then it must satisfy
yp=1+x+yp2+xyp
Thus 0=HH2+2ypH+1H2+xH
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