81.3.22 problem 22

Internal problem ID [18640]
Book : A short course on differential equations. By Donald Francis Campbell. Maxmillan company. London. 1907
Section : Chapter III. Ordinary differential equations of the first order and first degree. Exercises at page 33
Problem number : 22
Date solved : Tuesday, January 28, 2025 at 12:05:18 PM
CAS classification : [[_homogeneous, `class A`], _rational, [_Abel, `2nd type`, `class B`]]

\begin{align*} x \left (x -2 y\right ) y^{\prime }+x^{2}+2 y^{2}&=0 \end{align*}

✓ Solution by Maple

Time used: 0.017 (sec). Leaf size: 22

dsolve(x*(x-2*y(x))*diff(y(x),x)+(x^2+2*y(x)^2)=0,y(x), singsol=all)
 

\[ y \left (x \right ) = x \left (-1-\frac {3 \operatorname {LambertW}\left (-\frac {2 \,{\mathrm e}^{-\frac {2}{3}-\frac {c_{1}}{3}}}{3 x^{{1}/{3}}}\right )}{2}\right ) \]

✓ Solution by Mathematica

Time used: 7.823 (sec). Leaf size: 39

DSolve[x*(x-2*y[x])*D[y[x],x]+(x^2+2*y[x]^2)==0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to -\frac {1}{2} x \left (2+3 W\left (-\frac {2 e^{-\frac {c_1}{3}}}{3 \sqrt [3]{x}}\right )\right ) \\ y(x)\to -x \\ \end{align*}