Internal problem ID [2694]
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: 59.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_1st_order, _with_exponential_symmetries]]
Solve \begin {gather*} \boxed {1+\left (-y^{2}+x \right ) y^{\prime }=0} \end {gather*}
✓ Solution by Maple
Time used: 0.005 (sec). Leaf size: 24
dsolve(1+(x-y(x)^2)*diff(y(x),x)=0,y(x), singsol=all)
\[ x -y \relax (x )^{2}+2 y \relax (x )-2-{\mathrm e}^{-y \relax (x )} c_{1} = 0 \]
✓ Solution by Mathematica
Time used: 0.117 (sec). Leaf size: 24
DSolve[1+(x-y[x]^2)*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [x=y(x)^2-2 y(x)+c_1 e^{-y(x)}+2,y(x)\right ] \]