Internal problem ID [2623]
Book: Differential equations with applications and historial notes, George F. Simmons,
1971
Section: Chapter 2, End of chapter, page 61
Problem number: 24.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_exact]
Solve \begin {gather*} \boxed {\left ({\mathrm e}^{y} x +y-x^{2}\right ) y^{\prime }-2 y x +{\mathrm e}^{y}+x=0} \end {gather*}
✓ Solution by Maple
Time used: 0.012 (sec). Leaf size: 28
dsolve((x*exp(y(x))+y(x)-x^2)*diff(y(x),x)=(2*x*y(x) -exp(y(x))-x),y(x), singsol=all)
\[ -x^{2} y \relax (x )+{\mathrm e}^{y \relax (x )} x +\frac {x^{2}}{2}+\frac {y \relax (x )^{2}}{2}+c_{1} = 0 \]
✓ Solution by Mathematica
Time used: 0.332 (sec). Leaf size: 35
DSolve[(x*Exp[y[x]]+y[x]-x^2)*y'[x]==(2*x*y[x] -Exp[y[x]]-x),y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [x^2 (-y(x))+\frac {x^2}{2}+x e^{y(x)}+\frac {y(x)^2}{2}=c_1,y(x)\right ] \]