87.3.13 problem 13

Internal problem ID [23262]
Book : Ordinary differential equations with modern applications. Ladas, G. E. and Finizio, N. Wadsworth Publishing. California. 1978. ISBN 0-534-00552-7. QA372.F56
Section : Chapter 1. Elementary methods. First order differential equations. Exercise at page 26
Problem number : 13
Date solved : Thursday, October 02, 2025 at 09:27:20 PM
CAS classification : [_rational]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 78

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

\[ c_1 -\frac {-\operatorname {BesselI}\left (\frac {2}{5}, \frac {2 \sqrt {3}}{5 y^{{5}/{2}}}\right ) \sqrt {y}\, \sqrt {3}-\operatorname {BesselI}\left (-\frac {3}{5}, \frac {2 \sqrt {3}}{5 y^{{5}/{2}}}\right ) x}{-\operatorname {BesselK}\left (\frac {2}{5}, \frac {2 \sqrt {3}}{5 y^{{5}/{2}}}\right ) \sqrt {y}\, \sqrt {3}+\operatorname {BesselK}\left (\frac {3}{5}, \frac {2 \sqrt {3}}{5 y^{{5}/{2}}}\right ) x} = 0 \]

✗ Mathematica

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

Not solved

✗ Sympy

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

Timed Out