28.1.58 problem 59

Internal problem ID [4364]
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
Date solved : Monday, January 27, 2025 at 09:09:16 AM
CAS classification : [[_1st_order, _with_exponential_symmetries]]

\begin{align*} 1+\left (x -y^{2}\right ) y^{\prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.007 (sec). Leaf size: 24

dsolve(1+(x-y(x)^2)*diff(y(x),x)=0,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.122 (sec). Leaf size: 24

DSolve[1+(x-y[x]^2)*D[y[x],x]==0,y[x],x,IncludeSingularSolutions -> True]
 

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