78.8.43 problem 43

Internal problem ID [18170]
Book : DIFFERENTIAL EQUATIONS WITH APPLICATIONS AND HISTORICAL NOTES by George F. Simmons. 3rd edition. 2017. CRC press, Boca Raton FL.
Section : Chapter 2. First order equations. Miscellaneous Problems for Chapter 2. Problems at page 99
Problem number : 43
Date solved : Monday, March 31, 2025 at 05:20:58 PM
CAS classification : [[_homogeneous, `class A`], _rational, _Riccati]

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

✓ Maple. Time used: 0.004 (sec). Leaf size: 11

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

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

✓ Mathematica. Time used: 0.183 (sec). Leaf size: 13

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

\[ y(x)\to x \tan (\log (x)+c_1) \]

✓ Sympy. Time used: 0.274 (sec). Leaf size: 27

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

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