83.8.28 problem 29

Internal problem ID [19154]
Book : A Text book for differentional equations for postgraduate students by Ray and Chaturvedi. First edition, 1958. BHASKAR press. INDIA
Section : Chapter II. Equations of first order and first degree. Misc examples on chapter II at page 25
Problem number : 29
Date solved : Tuesday, January 28, 2025 at 01:10:08 PM
CAS classification : [[_homogeneous, `class A`], _rational, [_Abel, `2nd type`, `class B`]]

\begin{align*} y^{2}+x^{2} y^{\prime }&=x y y^{\prime } \end{align*}

Solution by Maple

Time used: 0.023 (sec). Leaf size: 17

dsolve(y(x)^2+x^2*diff(y(x),x)=x*y(x)*diff(y(x),x),y(x), singsol=all)
 
\[ y \left (x \right ) = -x \operatorname {LambertW}\left (-\frac {{\mathrm e}^{-c_{1}}}{x}\right ) \]

Solution by Mathematica

Time used: 2.070 (sec). Leaf size: 25

DSolve[y[x]^2+x^2*D[y[x],x]==x*y[x]*D[y[x],x],y[x],x,IncludeSingularSolutions -> True]
 
\begin{align*} y(x)\to -x W\left (-\frac {e^{-c_1}}{x}\right ) \\ y(x)\to 0 \\ \end{align*}