40.6.7 problem 16

Internal problem ID [6687]
Book : Schaums Outline. Theory and problems of Differential Equations, 1st edition. Frank Ayres. McGraw Hill 1952
Section : Chapter 10. Singular solutions, Extraneous loci. Supplemetary problems. Page 74
Problem number : 16
Date solved : Sunday, March 30, 2025 at 11:18:19 AM
CAS classification : [[_1st_order, _with_linear_symmetries], _dAlembert]

\begin{align*} 2 y&={y^{\prime }}^{2}+4 x y^{\prime } \end{align*}

✓ Maple. Time used: 0.027 (sec). Leaf size: 692

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

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

✓ Mathematica. Time used: 60.239 (sec). Leaf size: 1344

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

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

✗ Sympy

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

NotImplementedError : The given ODE 2*x - sqrt(4*x**2 + 2*y(x)) + Derivative(y(x), x) cannot be solved by the factorable group method