Internal problem ID [2058]
Book: Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath.
Boston. 1964
Section: Exercise 12, page 46
Problem number: 27.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_exact]
\[ \boxed {-2 y x +{\mathrm e}^{y}+\left (y-x^{2}+{\mathrm e}^{y} x \right ) y^{\prime }=-x} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 28
dsolve((x-2*x*y(x)+exp(y(x)) )+(y(x)-x^2+x*exp(y(x)) )*diff(y(x),x)=0,y(x), singsol=all)
\[ -x^{2} y \left (x \right )+{\mathrm e}^{y \left (x \right )} x +\frac {x^{2}}{2}+\frac {y \left (x \right )^{2}}{2}+c_{1} = 0 \]
✓ Solution by Mathematica
Time used: 0.306 (sec). Leaf size: 35
DSolve[(x-2*x*y[x]+Exp[y[x]] )+(y[x]-x^2+x*Exp[y[x]] )*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [x^2 (-y(x))+\frac {x^2}{2}+x e^{y(x)}+\frac {y(x)^2}{2}=c_1,y(x)\right ] \]