40.3.25 problem 25 (j)

Internal problem ID [6629]
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 : Wednesday, March 05, 2025 at 01:34:00 AM
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: 0.142 (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: 57.79 (sec). Leaf size: 452

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

\begin{align*} y(x)\to \frac {e^{-6 c_1} \sqrt [3]{-2 e^{12 c_1} x^6+2 \sqrt {-e^{24 c_1} x^6 \left (-x^6+e^{6 c_1}\right )}+e^{18 c_1}}+\frac {e^{6 c_1}}{\sqrt [3]{-2 e^{12 c_1} x^6+2 \sqrt {-e^{24 c_1} x^6 \left (-x^6+e^{6 c_1}\right )}+e^{18 c_1}}}+1}{2 x^2} \\ y(x)\to \frac {i \left (\sqrt {3}+i\right ) e^{-6 c_1} \sqrt [3]{-2 e^{12 c_1} x^6+2 \sqrt {-e^{24 c_1} x^6 \left (-x^6+e^{6 c_1}\right )}+e^{18 c_1}}-\frac {\left (1+i \sqrt {3}\right ) e^{6 c_1}}{\sqrt [3]{-2 e^{12 c_1} x^6+2 \sqrt {-e^{24 c_1} x^6 \left (-x^6+e^{6 c_1}\right )}+e^{18 c_1}}}+2}{4 x^2} \\ y(x)\to \frac {-\left (\left (1+i \sqrt {3}\right ) e^{-6 c_1} \sqrt [3]{-2 e^{12 c_1} x^6+2 \sqrt {-e^{24 c_1} x^6 \left (-x^6+e^{6 c_1}\right )}+e^{18 c_1}}\right )+\frac {i \left (\sqrt {3}+i\right ) e^{6 c_1}}{\sqrt [3]{-2 e^{12 c_1} x^6+2 \sqrt {-e^{24 c_1} x^6 \left (-x^6+e^{6 c_1}\right )}+e^{18 c_1}}}+2}{4 x^2} \\ y(x)\to 0 \\ y(x)\to \frac {3}{2 x^2} \\ \end{align*}

✗ 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