Internal problem ID [4055]
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]
Solve \begin {gather*} \boxed {2 x y y^{\prime }+3 x^{2}-y^{2}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.004 (sec). Leaf size: 31
dsolve(2*x*y(x)*diff(y(x),x)+3*x^2-y(x)^2=0,y(x), singsol=all)
\begin{align*} y \relax (x ) = \sqrt {c_{1} x -3 x^{2}} \\ y \relax (x ) = -\sqrt {c_{1} x -3 x^{2}} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.291 (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*}