50.1.10 problem 1(k)

Internal problem ID [7782]
Book : Differential Equations: Theory, Technique, and Practice by George Simmons, Steven Krantz. McGraw-Hill NY. 2007. 1st Edition.
Section : Chapter 1. What is a differential equation. Section 1.2 THE NATURE OF SOLUTIONS. Page 9
Problem number : 1(k)
Date solved : Monday, January 27, 2025 at 03:22:41 PM
CAS classification : [[_homogeneous, `class A`], _rational, _Bernoulli]

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

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 23

dsolve(2*x*y(x)*diff(y(x),x)=x^2+y(x)^2,y(x), singsol=all)
 

\begin{align*} y &= \sqrt {\left (x +c_{1} \right ) x} \\ y &= -\sqrt {\left (x +c_{1} \right ) x} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.210 (sec). Leaf size: 38

DSolve[2*x*y[x]*D[y[x],x]==x^2+y[x]^2,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to -\sqrt {x} \sqrt {x+c_1} \\ y(x)\to \sqrt {x} \sqrt {x+c_1} \\ \end{align*}