86.2.3 problem 3

Internal problem ID [23077]
Book : An introduction to Differential Equations. By Howard Frederick Cleaves. 1969. Oliver and Boyd publisher. ISBN 0050015044
Section : Chapter 3. Some standard types of differential equations. Exercise 3c at page 50
Problem number : 3
Date solved : Thursday, October 02, 2025 at 09:19:04 PM
CAS classification : [[_homogeneous, `class G`], _rational]

\begin{align*} y-x y^{\prime }&=3 y^{2} y^{\prime } \end{align*}

With initial conditions

\begin{align*} y \left (3\right )&=1 \\ \end{align*}

✓ Maple. Time used: 0.113 (sec). Leaf size: 12

ode:=y(x)-x*diff(y(x),x) = 3*y(x)^2*diff(y(x),x); 
ic:=[y(3) = 1]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

\[ y = \frac {\sqrt {3}\, \sqrt {x}}{3} \]

✓ Mathematica. Time used: 0.198 (sec). Leaf size: 16

ode=y[x]-x*D[y[x],x]==3*y[x]^2*D[y[x],x]; 
ic={y[3]==1}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {\sqrt {x}}{\sqrt {3}} \end{align*}

✓ Sympy. Time used: 0.477 (sec). Leaf size: 14

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-x*Derivative(y(x), x) - 3*y(x)**2*Derivative(y(x), x) + y(x),0) 
ics = {y(3): 1} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \frac {\sqrt {3} \sqrt {x}}{3} \]