89.9.3 problem 3

Internal problem ID [24483]
Book : A short course in Differential Equations. Earl D. Rainville. Second edition. 1958. Macmillan Publisher, NY. CAT 58-5010
Section : Chapter 4. Additional topics on equations of first order and first degree. Exercises at page 72
Problem number : 3
Date solved : Thursday, October 02, 2025 at 10:42:08 PM
CAS classification : [_rational, [_Abel, `2nd type`, `class B`]]

\begin{align*} y \left (1+2 x -y\right )+x \left (3 x -4 y+3\right ) y^{\prime }&=0 \end{align*}

✓ Maple. Time used: 0.005 (sec). Leaf size: 22

ode:=y(x)*(2*x-y(x)+1)+x*(3*x-4*y(x)+3)*diff(y(x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ -y^{4} x +\left (x^{2}+x \right ) y^{3}+c_1 = 0 \]

✓ Mathematica. Time used: 61.398 (sec). Leaf size: 1569

ode=y[x]*( 2*x-y[x]+1)+x*( 3*x-4*y[x]+3  )*D[y[x],x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

Too large to display

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x*(3*x - 4*y(x) + 3)*Derivative(y(x), x) + (2*x - y(x) + 1)*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out