34.2.2 problem 2

Internal problem ID [6032]
Book : A treatise on ordinary and partial differential equations by William Woolsey Johnson. 1913
Section : Chapter 2, Equations of the first order and degree. page 20
Problem number : 2
Date solved : Wednesday, March 05, 2025 at 12:10:04 AM
CAS classification : [_separable]

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

✓ Maple. Time used: 0.003 (sec). Leaf size: 17

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

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

✓ Mathematica. Time used: 0.135 (sec). Leaf size: 24

ode=D[y[x],x]==a*y[x]^2*x; 
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: 0.159 (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)
 

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