77.21.5 problem 5

Internal problem ID [20534]
Book : A Text book for differentional equations for postgraduate students by Ray and Chaturvedi. First edition, 1958. BHASKAR press. INDIA
Section : Chapter IV. Equations of the first order but not of the first degree. Exercise IV (D) at page 57
Problem number : 5
Date solved : Thursday, October 02, 2025 at 06:04:36 PM
CAS classification : [[_1st_order, _with_linear_symmetries], _rational, _Clairaut]

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

✓ Maple. Time used: 0.487 (sec). Leaf size: 22

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

\[ y = c_1 x +\sqrt {-a^{2} c_1^{2}+b^{2}} \]

✓ Mathematica. Time used: 0.243 (sec). Leaf size: 38

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

\begin{align*} y(x)&\to \sqrt {b^2-a^2 c_1{}^2}+c_1 x\\ y(x)&\to \sqrt {b^2} \end{align*}

✗ Sympy

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

Timed Out