Internal problem ID [4563]
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 12.42, page 103.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class A`], _rational, _Bernoulli]
\[ \boxed {2 x y y^{\prime }-y^{2}=-3 x^{2}} \]
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 29
dsolve(2*x*y(x)*diff(y(x),x)+3*x^2-y(x)^2=0,y(x), singsol=all)
\begin{align*} y \left (x \right ) &= \sqrt {\left (-3 x +c_{1} \right ) x} \\ y \left (x \right ) &= -\sqrt {c_{1} x -3 x^{2}} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.306 (sec). Leaf size: 35
DSolve[2*x*y[x]*y'[x]+3*x^2-y[x]^2==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\sqrt {x (-3 x+c_1)} \\ y(x)\to \sqrt {x (-3 x+c_1)} \\ \end{align*}