15.20.15 problem 15

Internal problem ID [3323]
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 : 15
Date solved : Sunday, March 30, 2025 at 01:35:48 AM
CAS classification : [[_1st_order, _with_linear_symmetries], _dAlembert]

\begin{align*} \frac {1}{{y^{\prime }}^{2}}+y^{\prime } x&=2 y \end{align*}

✓ Maple. Time used: 0.033 (sec). Leaf size: 1429

ode:=1/diff(y(x),x)^2+x*diff(y(x),x) = 2*y(x); 
dsolve(ode,y(x), singsol=all);
 

\begin{align*} \text {Solution too large to show}\end{align*}

✓ Mathematica. Time used: 152.672 (sec). Leaf size: 10773

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

Too large to display

✗ Sympy

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

Timed Out