29.25.32 problem 729

Internal problem ID [5319]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 25
Problem number : 729
Date solved : Tuesday, March 04, 2025 at 09:22:05 PM
CAS classification : [[_homogeneous, `class A`], _rational, _dAlembert]

\begin{align*} \left (x -\sqrt {x^{2}+y^{2}}\right ) y^{\prime }&=y \end{align*}

✓ Maple. Time used: 0.092 (sec). Leaf size: 18

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

\[ -c_{1} +\sqrt {x^{2}+y \left (x \right )^{2}}+x = 0 \]

✓ Mathematica. Time used: 0.49 (sec). Leaf size: 57

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

\begin{align*} y(x)\to -e^{\frac {c_1}{2}} \sqrt {-2 x+e^{c_1}} \\ y(x)\to e^{\frac {c_1}{2}} \sqrt {-2 x+e^{c_1}} \\ y(x)\to 0 \\ \end{align*}

✓ Sympy. Time used: 2.430 (sec). Leaf size: 12

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

\[ \log {\left (y{\left (x \right )} \right )} = C_{1} - \operatorname {asinh}{\left (\frac {x}{y{\left (x \right )}} \right )} \]