Internal problem ID [12155]
Book: DIFFERENTIAL and INTEGRAL CALCULUS. VOL I. by N. PISKUNOV. MIR
PUBLISHERS, Moscow 1969.
Section: Chapter 8. Differential equations. Exercises page 595
Problem number: 77.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type
[[_homogeneous, `class A`], _exact, _rational, [_Abel, `2nd type`, `class C`], _dAlembert]
\[ \boxed {\frac {x}{\left (x +y\right )^{2}}+\frac {\left (2 x +y\right ) y^{\prime }}{\left (x +y\right )^{2}}=0} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 19
dsolve(x/(x+y(x))^2+(2*x+y(x))/(x+y(x))^2*diff(y(x),x)=0,y(x), singsol=all)
\[ y \left (x \right ) = -\frac {x \left (\operatorname {LambertW}\left (c_{1} x \right )-1\right )}{\operatorname {LambertW}\left (c_{1} x \right )} \]
✓ Solution by Mathematica
Time used: 0.192 (sec). Leaf size: 33
DSolve[x/(x+y[x])^2+(2*x+y[x])/(x+y[x])^2*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [\log \left (\frac {y(x)}{x}+1\right )-\frac {1}{\frac {y(x)}{x}+1}=-\log (x)+c_1,y(x)\right ] \]