30.1.9 problem example page 47

Internal problem ID [5697]
Book : Differential and integral calculus, vol II By N. Piskunov. 1974
Section : Chapter 1
Problem number : example page 47
Date solved : Sunday, March 30, 2025 at 10:02:48 AM
CAS classification : [_Clairaut]

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

✓ Maple. Time used: 1.861 (sec). Leaf size: 17

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

\[ y = c_1 \left (x +\frac {a}{\sqrt {c_1^{2}+1}}\right ) \]

✓ Mathematica. Time used: 35.87 (sec). Leaf size: 27

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

\begin{align*} y(x)\to c_1 \left (x+\frac {a}{\sqrt {1+c_1{}^2}}\right ) \\ y(x)\to 0 \\ \end{align*}

✗ Sympy

from sympy import * 
x = symbols("x") 
a = symbols("a") 
y = Function("y") 
ode = Eq(-a*Derivative(y(x), x)/sqrt(Derivative(y(x), x)**2 + 1) - x*Derivative(y(x), x) + y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out