Internal problem ID [4024]
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 12.11, page 103.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class G], _rational, _Bernoulli]
Solve \begin {gather*} \boxed {x^{2} y+y^{2}+y^{\prime } x^{3}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 19
dsolve((x^2*y(x)+y(x)^2)+x^3*diff(y(x),x)=0,y(x), singsol=all)
\[ y \relax (x ) = \frac {3 x^{2}}{3 x^{3} c_{1}-1} \]
✓ Solution by Mathematica
Time used: 0.244 (sec). Leaf size: 26
DSolve[(x^2*y[x]+y[x]^2)+x^3*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {3 x^2}{-1+3 c_1 x^3} \\ y(x)\to 0 \\ \end{align*}