"P(x,y)=bxe^{2xy};Q(x,y)=ye^{2xy}+x"
"P_x=be^{2xy}+2bye^{2xy}"
"Q_y=e^{2xy}+2xye^{2xy}"
The equation is exact if "P_x=Q_y", hence
"be^{2xy}(1+2xy)=e^{2xy}(1+2xy)"
"b=1"
The solution of the equation "R(x,y)=const" , where
"R=\\int Pdy=\\int xe^{2xy}dy=\\frac{e^{2xy}}{2}+h(x)"
"R_x=Q" hence
"ye^{2xy}+h'=ye^{2xy}+x"
"h'=x"
"h=\\frac{x^2}{2}"
The solution of the equation
"\\frac{1}{2}(e^{2xy}+x^2)=const"
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