89.2.29 problem 31

Internal problem ID [24294]
Book : A short course in Differential Equations. Earl D. Rainville. Second edition. 1958. Macmillan Publisher, NY. CAT 58-5010
Section : Chapter 2. Equations of the first order and first degree. Exercises at page 27
Problem number : 31
Date solved : Thursday, October 02, 2025 at 10:08:20 PM
CAS classification : [[_homogeneous, `class A`], _rational, [_Abel, `2nd type`, `class B`]]

\begin{align*} y \left (9 x -2 y\right )-x \left (6 x -y\right ) y^{\prime }&=0 \end{align*}

With initial conditions

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

✓ Maple. Time used: 0.103 (sec). Leaf size: 18

ode:=y(x)*(9*x-2*y(x))-x*(6*x-y(x))*diff(y(x),x) = 0; 
ic:=[y(1) = 1]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

\[ y = \frac {\left (-x +\sqrt {x \left (x +24\right )}\right ) x}{4} \]

✓ Mathematica. Time used: 0.606 (sec). Leaf size: 28

ode=y[x]*( 9*x-2*y[x] )-x*( 6*x-y[x]  )*D[y[x],x]==0; 
ic={y[1]==1}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {1}{4} \left (x^{3/2} \sqrt {x+24}-x^2\right ) \end{align*}

✓ Sympy. Time used: 1.433 (sec). Leaf size: 19

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-x*(6*x - y(x))*Derivative(y(x), x) + (9*x - 2*y(x))*y(x),0) 
ics = {y(1): 1} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = - \frac {x^{2}}{4} + \frac {\sqrt {x^{3} \left (x + 24\right )}}{4} \]