Internal problem ID [12121]
Book: DIFFERENTIAL and INTEGRAL CALCULUS. VOL I. by N. PISKUNOV. MIR
PUBLISHERS, Moscow 1969.
Section: Chapter 8. Differential equations. Exercises page 595
Problem number: 41.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class A`], _rational, [_Abel, `2nd type`, `class A`]]
\[ \boxed {y+\left (y-x \right ) y^{\prime }=-x} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 24
dsolve((x+y(x))+(y(x)-x)*diff(y(x),x)=0,y(x), singsol=all)
\[ y \left (x \right ) = \tan \left (\operatorname {RootOf}\left (-2 \textit {\_Z} +\ln \left (\frac {1}{\cos \left (\textit {\_Z} \right )^{2}}\right )+2 \ln \left (x \right )+2 c_{1} \right )\right ) x \]
✓ Solution by Mathematica
Time used: 0.054 (sec). Leaf size: 36
DSolve[(x+y[x])+(y[x]-x)*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [\frac {1}{2} \log \left (\frac {y(x)^2}{x^2}+1\right )-\arctan \left (\frac {y(x)}{x}\right )=-\log (x)+c_1,y(x)\right ] \]