75.12.9 problem 283

Internal problem ID [16804]
Book : A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV, G.I. MARKARENKO. MIR, MOSCOW. 1983
Section : Section 12. Miscellaneous problems. Exercises page 93
Problem number : 283
Date solved : Monday, March 31, 2025 at 03:21:53 PM
CAS classification : [[_1st_order, _with_exponential_symmetries]]

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

✓ Maple. Time used: 0.005 (sec). Leaf size: 24

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

\[ x -\frac {y^{2}}{2}-\frac {y}{2}-\frac {1}{4}-{\mathrm e}^{2 y} c_1 = 0 \]

✓ Mathematica. Time used: 0.151 (sec). Leaf size: 42

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

\[ \text {Solve}\left [x=e^{2 y(x)} \int _1^{y(x)}-e^{-2 K[1]} K[1]^2dK[1]+c_1 e^{2 y(x)},y(x)\right ] \]

✗ Sympy

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

TypeError : NoneType object is not subscriptable