44.1.8 problem 1(i)

Internal problem ID [9066]
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(i)
Date solved : Tuesday, September 30, 2025 at 06:03:27 PM
CAS classification : [[_homogeneous, `class D`], _rational, _Riccati]

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

✓ Maple. Time used: 0.003 (sec). Leaf size: 10

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

\[ y = \tan \left (x +c_1 \right ) x \]

✓ Mathematica. Time used: 0.05 (sec). Leaf size: 28

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

\[ \text {Solve}\left [\int _1^{\frac {y(x)}{x}}\frac {1}{K[1]^2+1}dK[1]=x+c_1,y(x)\right ] \]

✓ Sympy. Time used: 0.197 (sec). Leaf size: 24

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

\[ y{\left (x \right )} = \frac {x \left (i C_{1} + i e^{2 i x}\right )}{C_{1} - e^{2 i x}} \]