15.8.26 problem 27

Internal problem ID [3029]
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
Date solved : Monday, January 27, 2025 at 07:09:28 AM
CAS classification : [_exact]

\begin{align*} x -2 y x +{\mathrm e}^{y}+\left (y-x^{2}+x \,{\mathrm e}^{y}\right ) y^{\prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.018 (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)
 

\[ -x^{2} y+x \,{\mathrm e}^{y}+\frac {x^{2}}{2}+\frac {y^{2}}{2}+c_{1} = 0 \]

✓ Solution by Mathematica

Time used: 0.364 (sec). Leaf size: 35

DSolve[(x-2*x*y[x]+Exp[y[x]] )+(y[x]-x^2+x*Exp[y[x]] )*D[y[x],x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ \text {Solve}\left [x^2 (-y(x))+\frac {x^2}{2}+x e^{y(x)}+\frac {y(x)^2}{2}=c_1,y(x)\right ] \]