71.1.28 problem 44 (page 55)

Internal problem ID [19204]
Book : V.V. Stepanov, A course of differential equations (in Russian), GIFML. Moscow (1958)
Section : All content
Problem number : 44 (page 55)
Date solved : Thursday, October 02, 2025 at 03:43:19 PM
CAS classification : [_rational, [_Riccati, _special]]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 20

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

\[ y = \frac {-x +\tan \left (-\frac {1}{x}+c_1 \right )}{x^{2}} \]

✓ Mathematica. Time used: 0.205 (sec). Leaf size: 76

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

\begin{align*} y(x)&\to -\frac {e^2 (x+i)+2 c_1 e^{2 i/x} (1+i x)}{x^2 \left (e^2+2 i c_1 e^{2 i/x}\right )}\\ y(x)&\to \frac {-x+i}{x^2} \end{align*}

✓ Sympy. Time used: 0.153 (sec). Leaf size: 39

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

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