77.1.26 problem 42 (page 55)

Internal problem ID [17837]
Book : V.V. Stepanov, A course of differential equations (in Russian), GIFML. Moscow (1958)
Section : All content
Problem number : 42 (page 55)
Date solved : Thursday, March 13, 2025 at 10:58:56 AM
CAS classification : [[_homogeneous, `class G`], _rational, _Riccati]

\begin{align*} y^{\prime }+y^{2}+\frac {y}{x}-\frac {4}{x^{2}}&=0 \end{align*}

✓ Maple. Time used: 20.542 (sec). Leaf size: 26

ode:=diff(y(x),x)+y(x)^2+y(x)/x-4/x^2 = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {-2 x^{4}-2 c_{1}}{x \left (-x^{4}+c_{1} \right )} \]

✓ Mathematica. Time used: 0.858 (sec). Leaf size: 63

ode=D[y[x],x]+y[x]^2+y[x]/x-4/x^2==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)\to \frac {2 i \tan (c_1-2 i \log (x))}{x} \\ y(x)\to \frac {2 \left (x^4-e^{2 i \text {Interval}[\{0,\pi \}]}\right )}{x \left (x^4+e^{2 i \text {Interval}[\{0,\pi \}]}\right )} \\ \end{align*}

✓ Sympy. Time used: 0.166 (sec). Leaf size: 19

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

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