Internal problem ID [3235]
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]
\[ \boxed {x y^{2} \left (x y^{\prime }+y\right )=1} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 74
dsolve(x*y(x)^2*(x*diff(y(x),x)+y(x) )=1,y(x), singsol=all)
\begin{align*} y \left (x \right ) &= \frac {\left (12 x^{2}+8 c_{1} \right )^{\frac {1}{3}}}{2 x} \\ y \left (x \right ) &= -\frac {\left (12 x^{2}+8 c_{1} \right )^{\frac {1}{3}} \left (1+i \sqrt {3}\right )}{4 x} \\ y \left (x \right ) &= \frac {\left (12 x^{2}+8 c_{1} \right )^{\frac {1}{3}} \left (i \sqrt {3}-1\right )}{4 x} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.233 (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*}