Internal problem ID [4039]
Book: Ordinary Differential Equations, By Tenenbaum and Pollard. Dover, NY 1963
Section: Chapter 2. Special types of differential equations of the first kind. Lesson 12, Miscellaneous
Methods
Problem number: Exercise 12.26, page 103.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class D], _rational, _Bernoulli]
Solve \begin {gather*} \boxed {y^{\prime } x^{3}-y^{2}-x^{2} y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 15
dsolve(x^3*diff(y(x),x)-y(x)^2-x^2*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = \frac {x^{2}}{c_{1} x +1} \]
✓ Solution by Mathematica
Time used: 0.21 (sec). Leaf size: 22
DSolve[x^3*y'[x]-y[x]^2-x^2*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {x^2}{1+c_1 x} \\ y(x)\to 0 \\ \end{align*}