Internal problem ID [15066]
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.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_exact]
\[ \boxed {\frac {x}{\sqrt {x^{2}+y^{2}}}+\frac {1}{y}+\left (\frac {y}{\sqrt {x^{2}+y^{2}}}+\frac {1}{y}-\frac {x}{y^{2}}\right ) y^{\prime }=-\frac {1}{x}} \]
✓ Solution by Maple
Time used: 0.0 (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)
\[ \frac {y \left (x \right ) \ln \left (y \left (x \right )\right )+\left (\sqrt {x^{2}+y \left (x \right )^{2}}+c_{1} +\ln \left (x \right )\right ) y \left (x \right )+x}{y \left (x \right )} = 0 \]
✗ Solution by Mathematica
Time used: 0.0 (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)*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
Not solved