Internal problem ID [1905]
Book: Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath.
Boston. 1964
Section: Exercise 6, page 25
Problem number: 6.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class A`], _rational, [_Abel, `2nd type`, `class A`]]
\[ \boxed {y y^{\prime }-2 y=-x} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 18
dsolve(x+y(x)*diff(y(x),x)=2*y(x),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: 0.118 (sec). Leaf size: 33
DSolve[x+y[x]*y'[x]==2*y[x],y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [\log \left (\frac {y(x)}{x}-1\right )-\frac {1}{\frac {y(x)}{x}-1}=-\log (x)+c_1,y(x)\right ] \]