8.5.2 problem 2

Internal problem ID [730]
Book : Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section : Section 1.6, Substitution methods and exact equations. Page 74
Problem number : 2
Date solved : Monday, January 27, 2025 at 02:59:25 AM
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: 0.003 (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: 0.172 (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*}