89.32.10 problem 11

Internal problem ID [24970]
Book : A short course in Differential Equations. Earl D. Rainville. Second edition. 1958. Macmillan Publisher, NY. CAT 58-5010
Section : Chapter 16. Equations of order one and higher degree. Miscellaneous Exercises at page 246
Problem number : 11
Date solved : Thursday, October 02, 2025 at 11:45:09 PM
CAS classification : [[_1st_order, _with_linear_symmetries], _dAlembert]

\begin{align*} {y^{\prime }}^{4}+x y^{\prime }-3 y&=0 \end{align*}

✓ Maple. Time used: 0.014 (sec). Leaf size: 34

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

\[ \left [x \left (\textit {\_T} \right ) = \frac {\sqrt {\textit {\_T}}\, \left (4 \textit {\_T}^{{5}/{2}}+5 c_1 \right )}{5}, y \left (\textit {\_T} \right ) = \frac {3 \textit {\_T}^{4}}{5}+\frac {\textit {\_T}^{{3}/{2}} c_1}{3}\right ] \]

✗ Mathematica

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

Timed out

✗ Sympy

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

Timed Out