88.7.8 problem 8
Internal
problem
ID
[24003]
Book
:
Elementary
Differential
Equations.
By
Lee
Roy
Wilcox
and
Herbert
J.
Curtis.
1961
first
edition.
International
texbook
company.
Scranton,
Penn.
USA.
CAT
number
61-15976
Section
:
Chapter
2.
Differential
equations
of
first
order.
Exercise
at
page
41
Problem
number
:
8
Date
solved
:
Thursday, October 02, 2025 at 09:52:05 PM
CAS
classification
:
[_exact, _rational, [_Abel, `2nd type`, `class B`]]
\begin{align*} \frac {1-6 x^{2} y}{x}+\frac {\left (2+5 y-3 x^{2} y\right ) y^{\prime }}{y}&=0 \end{align*}
✓ Maple. Time used: 0.035 (sec). Leaf size: 67
ode:=(1-6*x^2*y(x))/x+(2+5*y(x)-3*x^2*y(x))/y(x)*diff(y(x),x) = 0;
dsolve(ode,y(x), singsol=all);
\begin{align*}
y &= -\frac {2 \operatorname {LambertW}\left (-\frac {\sqrt {\frac {\left (3 x^{2}-5\right )^{2}}{x}}\, c_1}{2}\right )}{3 x^{2}-5} \\
y &= -\frac {2 \operatorname {LambertW}\left (\frac {\sqrt {\frac {\left (3 x^{2}-5\right )^{2}}{x}}\, c_1}{2}\right )}{3 x^{2}-5} \\
\end{align*}
✓ Mathematica. Time used: 8.595 (sec). Leaf size: 603
ode=( (1-6*x^2*y[x])/x )+( (2+5*y[x]-3*x^2*y[x])/y[x] )*D[y[x],{x,1}]==0;
ic={};
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
\[
\text {Solve}\left [\frac {\frac {2 \left (1-\frac {\left (9 x^2+5\right ) \left (\left (3 x^2-5\right ) y(x)+4\right )}{\left (3 x^2-5\right ) \sqrt [3]{\frac {\left (9 x^2+5\right )^3}{\left (3 x^2-5\right )^3}} \left (\left (3 x^2-5\right ) y(x)-2\right )}\right ) \left (\frac {\left (9 x^2+5\right ) \left (\left (3 x^2-5\right ) y(x)+4\right )}{\left (3 x^2-5\right ) \sqrt [3]{\frac {\left (9 x^2+5\right )^3}{\left (3 x^2-5\right )^3}} \left (\left (3 x^2-5\right ) y(x)-2\right )}+2\right ) \left (\left (1-\frac {\left (9 x^2+5\right ) \left (\left (3 x^2-5\right ) y(x)+4\right )}{\left (3 x^2-5\right ) \sqrt [3]{\frac {\left (9 x^2+5\right )^3}{\left (3 x^2-5\right )^3}} \left (\left (3 x^2-5\right ) y(x)-2\right )}\right ) \log \left (2^{2/3} \left (1-\frac {\left (9 x^2+5\right ) \left (\left (3 x^2-5\right ) y(x)+4\right )}{\left (3 x^2-5\right ) \sqrt [3]{\frac {\left (9 x^2+5\right )^3}{\left (3 x^2-5\right )^3}} \left (\left (3 x^2-5\right ) y(x)-2\right )}\right )\right )+\left (\frac {\left (9 x^2+5\right ) \left (\left (3 x^2-5\right ) y(x)+4\right )}{\left (3 x^2-5\right ) \sqrt [3]{\frac {\left (9 x^2+5\right )^3}{\left (3 x^2-5\right )^3}} \left (\left (3 x^2-5\right ) y(x)-2\right )}-1\right ) \log \left (2^{2/3} \left (\frac {\left (9 x^2+5\right ) \left (\left (3 x^2-5\right ) y(x)+4\right )}{\left (3 x^2-5\right ) \sqrt [3]{\frac {\left (9 x^2+5\right )^3}{\left (3 x^2-5\right )^3}} \left (\left (3 x^2-5\right ) y(x)-2\right )}+2\right )\right )-3\right )}{-\frac {\left (\left (3 x^2-5\right ) y(x)+4\right )^3}{\left (\left (3 x^2-5\right ) y(x)-2\right )^3}+\frac {3 \left (9 x^2+5\right ) \left (\left (3 x^2-5\right ) y(x)+4\right )}{\left (3 x^2-5\right ) \sqrt [3]{\frac {\left (9 x^2+5\right )^3}{\left (3 x^2-5\right )^3}} \left (\left (3 x^2-5\right ) y(x)-2\right )}-2}+\frac {\left (\frac {\left (9 x^2+5\right )^3}{\left (3 x^2-5\right )^3}\right )^{2/3} \left (5-3 x^2\right )^2 \left (\log (x)-2 \log \left (5-3 x^2\right )\right )}{\left (9 x^2+5\right )^2}}{9 \sqrt [3]{2}}=c_1,y(x)\right ]
\]
✗ Sympy
from sympy import *
x = symbols("x")
y = Function("y")
ode = Eq((-3*x**2*y(x) + 5*y(x) + 2)*Derivative(y(x), x)/y(x) + (-6*x**2*y(x) + 1)/x,0)
ics = {}
dsolve(ode,func=y(x),ics=ics)
Timed Out