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 : Wednesday, March 05, 2025 at 05:04:35 AM
CAS classification : [[_homogeneous, `class A`], _rational, _Bernoulli]

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

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

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

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

✓ Mathematica. Time used: 0.21 (sec). Leaf size: 38

ode=2*x*y[x]*D[y[x],x]==x^2+y[x]^2; 
ic={}; 
DSolve[{ode,ic},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*}

✓ Sympy. Time used: 0.378 (sec). Leaf size: 22

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-x**2 + 2*x*y(x)*Derivative(y(x), x) - y(x)**2,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ \left [ y{\left (x \right )} = - \sqrt {x \left (C_{1} + x\right )}, \ y{\left (x \right )} = \sqrt {x \left (C_{1} + x\right )}\right ] \]