69.2.20 problem 40

Internal problem ID [17984]
Book : A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV, G.I. MARKARENKO. MIR, MOSCOW. 1983
Section : Section 2. The method of isoclines. Exercises page 27
Problem number : 40
Date solved : Thursday, October 02, 2025 at 02:31:59 PM
CAS classification : [_quadrature]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 11

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

\[ y = \frac {1}{-x +c_1} \]

✓ Mathematica. Time used: 0.066 (sec). Leaf size: 18

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

\begin{align*} y(x)&\to -\frac {1}{x+c_1}\\ y(x)&\to 0 \end{align*}

✓ Sympy. Time used: 0.072 (sec). Leaf size: 8

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

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