15.5.20 problem 24

Internal problem ID [2956]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 9, page 38
Problem number : 24
Date solved : Sunday, March 30, 2025 at 01:01:19 AM
CAS classification : [[_1st_order, `_with_symmetry_[F(x),G(x)*y+H(x)]`]]

\begin{align*} y-x^{2} \sqrt {x^{2}-y^{2}}-x y^{\prime }&=0 \end{align*}

With initial conditions

\begin{align*} y \left (1\right )&=1 \end{align*}

✗ Maple

ode:=y(x)-x^2*(x^2-y(x)^2)^(1/2)-x*diff(y(x),x) = 0; 
ic:=y(1) = 1; 
dsolve([ode,ic],y(x), singsol=all);
 

\[ \text {No solution found} \]

✗ Mathematica

ode=(y[x]-x^2*Sqrt[x^2-y[x]^2])-x*D[y[x],x]==0; 
ic={y[1]==1}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

{}

✗ Sympy

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

Timed Out