81.15.11 problem 19-12

Internal problem ID [21719]
Book : The Differential Equations Problem Solver. VOL. I. M. Fogiel director. REA, NY. 1978. ISBN 78-63609
Section : Chapter 19. Change of variables. Page 483
Problem number : 19-12
Date solved : Thursday, October 02, 2025 at 08:01:11 PM
CAS classification : [[_homogeneous, `class D`], _rational, _Riccati]

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

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

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

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

✓ Mathematica. Time used: 0.126 (sec). Leaf size: 12

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

\begin{align*} y(x)&\to x \tan (x+c_1) \end{align*}

✓ Sympy. Time used: 0.180 (sec). Leaf size: 24

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

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