83.48.17 problem Ex 17 page 112

Internal problem ID [19538]
Book : A Text book for differentional equations for postgraduate students by Ray and Chaturvedi. First edition, 1958. BHASKAR press. INDIA
Section : Book Solved Excercises. Chapter VII. Exact differential equations.
Problem number : Ex 17 page 112
Date solved : Monday, March 31, 2025 at 07:32:25 PM
CAS classification : [[_2nd_order, _missing_x]]

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

✗ Maple

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

\[ \text {No solution found} \]

✗ Mathematica

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

Not solved

✗ Sympy

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

NotImplementedError : The given ODE Derivative(y(x), x) - (n*sqrt((-a**2*n**2 + a**2 + y(x)**2*Derivative(y(x), (x, 2)))*Derivative(y(x), (x, 2))) - y(x)*Derivative(y(x), (x, 2)))/(n**2 - 1) cannot be solved by the factorable group method