26.5.19 problem 24

Internal problem ID [4293]
Book : Differential equations with applications and historial notes, George F. Simmons. Second edition. 1971
Section : Chapter 2, End of chapter, page 61
Problem number : 24
Date solved : Monday, January 27, 2025 at 08:50:02 AM
CAS classification : [_exact]

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

✓ Solution by Maple

Time used: 0.007 (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)
 

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

✓ Solution by Mathematica

Time used: 0.344 (sec). Leaf size: 35

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

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