75.7.3 problem 177

Internal problem ID [16796]
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 : Tuesday, January 28, 2025 at 09:27:39 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*}

✓ Solution by Maple

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

dsolve((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)*diff(y(x),x)=0,y(x), singsol=all)
 

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

✗ Solution by Mathematica

Time used: 0.000 (sec). Leaf size: 0

DSolve[(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,y[x],x,IncludeSingularSolutions -> True]
 

Not solved