67.5.28 problem 6.7 (p)

Internal problem ID [16426]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 6. Simplifying through simplifiction. Additional exercises. page 114
Problem number : 6.7 (p)
Date solved : Thursday, October 02, 2025 at 01:31:28 PM
CAS classification : [[_homogeneous, `class G`], _rational, _Riccati]

\begin{align*} y^{\prime }&=x \left (1+\frac {2 y}{x^{2}}+\frac {y^{2}}{x^{4}}\right ) \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 16

ode:=diff(y(x),x) = x*(1+2/x^2*y(x)+y(x)^2/x^4); 
dsolve(ode,y(x), singsol=all);
 

\[ y = -\tan \left (-\ln \left (x \right )+c_1 \right ) x^{2} \]

✓ Mathematica. Time used: 0.132 (sec). Leaf size: 15

ode=D[y[x],x]==x*(1+2*y[x]/x^2+y[x]^2/x^4); 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to x^2 \tan (\log (x)+c_1) \end{align*}

✓ Sympy. Time used: 0.178 (sec). Leaf size: 29

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-x*(1 + 2*y(x)/x**2 + y(x)**2/x**4) + Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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