34.3.25 problem 25 (j)

Internal problem ID [7916]
Book : Schaums Outline. Theory and problems of Differential Equations, 1st edition. Frank Ayres. McGraw Hill 1952
Section : Chapter 5. Equations of first order and first degree (Exact equations). Supplemetary problems. Page 33
Problem number : 25 (j)
Date solved : Tuesday, September 30, 2025 at 05:10:01 PM
CAS classification : [[_homogeneous, `class G`], _rational, [_Abel, `2nd type`, `class B`]]

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

✓ Maple. Time used: 0.171 (sec). Leaf size: 673

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

\begin{align*} \text {Solution too large to show}\end{align*}

✓ Mathematica. Time used: 5.824 (sec). Leaf size: 89

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

\[ \text {Solve}\left [\int _1^{\frac {(-1)^{2/3} \left (x^2 y(x)-4\right )}{2^{2/3} \sqrt [3]{5} \left (x^2 y(x)-1\right )}}\frac {1}{K[1]^3+\frac {21 \sqrt [3]{-\frac {1}{2}} K[1]}{2\ 5^{2/3}}+1}dK[1]=\frac {2}{9} (-5)^{2/3} \sqrt [3]{2} \log (x)+c_1,y(x)\right ] \]

✗ Sympy

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

Timed Out