Internal problem ID [1975]
Book: Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath.
Boston. 1964
Section: Exercise 9, page 38
Problem number: 10.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class G`], _rational, [_Abel, `2nd type`, `class A`]]
\[ \boxed {2 y x +\left (-x^{2}+y\right ) y^{\prime }=0} \]
✓ Solution by Maple
Time used: 0.032 (sec). Leaf size: 18
dsolve(2*x*y(x)+(y(x)-x^2)*diff(y(x),x)=0,y(x), singsol=all)
\[ y \left (x \right ) = -\frac {x^{2}}{\operatorname {LambertW}\left (-c_{1} x^{2}\right )} \]
✓ Solution by Mathematica
Time used: 3.007 (sec). Leaf size: 285
DSolve[2*x*y[x]+(y[x]-x^2)*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [\frac {\left (2-\frac {2 \left (x^3+2 x y(x)\right )}{\sqrt [3]{x^3} \left (x^2-y(x)\right )}\right ) \left (\frac {x^3+2 x y(x)}{\sqrt [3]{x^3} \left (x^2-y(x)\right )}+2\right ) \left (\left (1-\frac {x \left (x^2+2 y(x)\right )}{\sqrt [3]{x^3} \left (x^2-y(x)\right )}\right ) \log \left (\frac {2-\frac {2 \left (x^3+2 x y(x)\right )}{\sqrt [3]{x^3} \left (x^2-y(x)\right )}}{\sqrt [3]{2}}\right )+\left (\frac {x^3+2 x y(x)}{\sqrt [3]{x^3} \left (x^2-y(x)\right )}-1\right ) \log \left (\frac {\frac {2 \left (x^3+2 x y(x)\right )}{\sqrt [3]{x^3} \left (x^2-y(x)\right )}+4}{\sqrt [3]{2}}\right )-3\right )}{9 \sqrt [3]{2} \left (-\frac {\left (x^2+2 y(x)\right )^3}{\left (x^2-y(x)\right )^3}+\frac {3 \left (x^3+2 x y(x)\right )}{\sqrt [3]{x^3} \left (x^2-y(x)\right )}-2\right )}=\frac {2\ 2^{2/3} x \log (x)}{9 \sqrt [3]{x^3}}+c_1,y(x)\right ] \]