75.7.3 problem 177

Internal problem ID [16717]
Book : A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV, G.I. MARKARENKO. MIR, MOSCOW. 1983
Section : Section 7, Total differential equations. The integrating factor. Exercises page 61
Problem number : 177
Date solved : Friday, March 14, 2025 at 04:48:51 AM
CAS classification : [_exact]

\begin{align*} \frac {x}{\sqrt {x^{2}+y^{2}}}+\frac {1}{x}+\frac {1}{y}+\left (\frac {y}{\sqrt {x^{2}+y^{2}}}+\frac {1}{y}-\frac {x}{y^{2}}\right ) y^{\prime }&=0 \end{align*}

✓ Maple. Time used: 0.006 (sec). Leaf size: 33

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

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

✗ Mathematica

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

Not solved

✗ Sympy

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

Timed Out