32.6.42 problem Exercise 12.42, page 103

Internal problem ID [5907]
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
Date solved : Monday, January 27, 2025 at 01:25:41 PM
CAS classification : [[_homogeneous, `class A`], _rational, _Bernoulli]

\begin{align*} 2 x y y^{\prime }+3 x^{2}-y^{2}&=0 \end{align*}

✓ Solution by Maple

Time used: 0.006 (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: 0.395 (sec). Leaf size: 35

DSolve[2*x*y[x]*D[y[x],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*}