77.1.9 problem 20 (page 30)

Internal problem ID [17899]
Book : V.V. Stepanov, A course of differential equations (in Russian), GIFML. Moscow (1958)
Section : All content
Problem number : 20 (page 30)
Date solved : Tuesday, January 28, 2025 at 11:11:02 AM
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: 0.130 (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)
 

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

✓ Solution by Mathematica

Time used: 1.982 (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*}