Internal problem ID [3188]
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: 44.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class G`], _rational, [_Abel, `2nd type`, `class B`]]
\[ \boxed {y^{2}-\left (y x +x^{3}\right ) y^{\prime }=0} \]
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 35
dsolve((y(x)^2)-(x*y(x)+x^3)*diff(y(x),x)=0,y(x), singsol=all)
\begin{align*} y \left (x \right ) = \left (-x -\sqrt {x^{2}+c_{1}}\right ) x y \left (x \right ) = \left (-x +\sqrt {x^{2}+c_{1}}\right ) x \end{align*}
✓ Solution by Mathematica
Time used: 0.551 (sec). Leaf size: 67
DSolve[(y[x]^2)-(x*y[x]+x^3)*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -x^2 \left (1+\sqrt {\frac {1}{x^3}} \sqrt {x \left (x^2+c_1\right )}\right ) y(x)\to x^2 \left (-1+\sqrt {\frac {1}{x^3}} \sqrt {x \left (x^2+c_1\right )}\right ) y(x)\to 0 \end{align*}