15.20.13 problem 13

Internal problem ID [3321]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 38, page 173
Problem number : 13
Date solved : Friday, March 14, 2025 at 01:27:22 AM
CAS classification : [[_1st_order, _with_linear_symmetries], _dAlembert]

\begin{align*} 3 {y^{\prime }}^{4} x&={y^{\prime }}^{3} y+1 \end{align*}

✓ Maple. Time used: 0.042 (sec). Leaf size: 34

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

\[ \left [x \left (\textit {\_T} \right ) = \frac {5 c_{1} \textit {\_T}^{{5}/{2}}+3}{5 \textit {\_T}^{4}}, y \left (\textit {\_T} \right ) = \frac {15 c_{1} \textit {\_T}^{{5}/{2}}+4}{5 \textit {\_T}^{3}}\right ] \]

✗ Mathematica

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

Timed out

✗ Sympy

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

Timed Out