Internal problem ID [2726]
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: 111.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class G], _rational, _Bernoulli]
Solve \begin {gather*} \boxed {x y^{2} \left (y^{\prime } x +y\right )-1=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 96
dsolve(x*y(x)^2*(x*diff(y(x),x)+y(x) )=1,y(x), singsol=all)
\begin{align*} y \relax (x ) = \frac {\left (12 x^{2}+8 c_{1}\right )^{\frac {1}{3}}}{2 x} \\ y \relax (x ) = \frac {-\frac {\left (12 x^{2}+8 c_{1}\right )^{\frac {1}{3}}}{4}-\frac {i \sqrt {3}\, \left (12 x^{2}+8 c_{1}\right )^{\frac {1}{3}}}{4}}{x} \\ y \relax (x ) = \frac {-\frac {\left (12 x^{2}+8 c_{1}\right )^{\frac {1}{3}}}{4}+\frac {i \sqrt {3}\, \left (12 x^{2}+8 c_{1}\right )^{\frac {1}{3}}}{4}}{x} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.252 (sec). Leaf size: 80
DSolve[x*y[x]^2*(x*y'[x]+y[x])==1,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {\sqrt [3]{-\frac {1}{2}} \sqrt [3]{3 x^2+2 c_1}}{x} \\ y(x)\to \frac {\sqrt [3]{\frac {3 x^2}{2}+c_1}}{x} \\ y(x)\to \frac {(-1)^{2/3} \sqrt [3]{\frac {3 x^2}{2}+c_1}}{x} \\ \end{align*}