Internal problem ID [2679]
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]]
Solve \begin {gather*} \boxed {y^{2}-\left (y x +x^{3}\right ) y^{\prime }=0} \end {gather*}
✓ Solution by Maple
Time used: 0.02 (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 \relax (x ) = \left (-x -\sqrt {x^{2}+c_{1}}\right ) x \\ y \relax (x ) = \left (-x +\sqrt {x^{2}+c_{1}}\right ) x \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.438 (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*}