28.1.37 problem 37

Internal problem ID [4343]
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 : 37
Date solved : Monday, January 27, 2025 at 09:06:16 AM
CAS classification : [_rational]

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

✓ Solution by Maple

Time used: 0.034 (sec). Leaf size: 28

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

\[ y \left (x \right ) = {\mathrm e}^{\operatorname {RootOf}\left (x^{2} {\mathrm e}^{\textit {\_Z}}+{\mathrm e}^{2 \textit {\_Z}}+c_{1} {\mathrm e}^{\textit {\_Z}}+\textit {\_Z} \,{\mathrm e}^{\textit {\_Z}}-x \right )} \]

✓ Solution by Mathematica

Time used: 0.182 (sec). Leaf size: 22

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

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