23.1.74 problem 68

Internal problem ID [4681]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Part II. Chapter 1. THE DIFFERENTIAL EQUATION IS OF FIRST ORDER AND OF FIRST DEGREE, page 223
Problem number : 68
Date solved : Tuesday, September 30, 2025 at 07:58:15 AM
CAS classification : [_separable]

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

✓ Maple. Time used: 0.001 (sec). Leaf size: 17

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

\[ y = -\frac {2}{a \,x^{2}-2 c_1} \]

✓ Mathematica. Time used: 0.086 (sec). Leaf size: 24

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

\begin{align*} y(x)&\to -\frac {2}{a x^2+2 c_1}\\ y(x)&\to 0 \end{align*}

✓ Sympy. Time used: 0.083 (sec). Leaf size: 12

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

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