1.62 problem 63

Internal problem ID [2698]

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]]

Solve \begin {gather*} \boxed {y+\left (y^{2} {\mathrm e}^{y}-x \right ) y^{\prime }=0} \end {gather*}

Solution by Maple

Time used: 0.017 (sec). Leaf size: 16

dsolve(y(x)+(y(x)^2*exp(y(x))-x)*diff(y(x),x)=0,y(x), singsol=all)
 

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

Solution by Mathematica

Time used: 0.212 (sec). Leaf size: 19

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

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