Internal problem ID [3207]
Book: Differential equations for engineers by Wei-Chau XIE, Cambridge Press 2010
Section: Chapter 2. First-Order and Simple Higher-Order Differential Equations. Page
78
Problem number: 63.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_1st_order, _with_linear_symmetries]]
\[ \boxed {y+\left (y^{2} {\mathrm e}^{y}-x \right ) y^{\prime }=0} \]
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 16
dsolve(y(x)+(y(x)^2*exp(y(x))-x)*diff(y(x),x)=0,y(x), singsol=all)
\[ {\mathrm e}^{y \left (x \right )} y \left (x \right )-c_{1} y \left (x \right )+x = 0 \]
✓ Solution by Mathematica
Time used: 0.195 (sec). Leaf size: 19
DSolve[y[x]+(y[x]^2*Exp[y[x]]-x)*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [x=-e^{y(x)} y(x)+c_1 y(x),y(x)\right ] \]