38.2.35 problem 35

Internal problem ID [6464]
Book : Engineering Mathematics. By K. A. Stroud. 5th edition. Industrial press Inc. NY. 2001
Section : Program 24. First order differential equations. Further problems 24. page 1068
Problem number : 35
Date solved : Monday, January 27, 2025 at 02:06:15 PM
CAS classification : [[_homogeneous, `class A`], _rational, [_Abel, `2nd type`, `class B`]]

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

With initial conditions

\begin{align*} y \left (1\right )&=1 \end{align*}

✓ Solution by Maple

Time used: 0.186 (sec). Leaf size: 13

dsolve([x^2*diff(y(x),x)=y(x)^2-x*y(x)*diff(y(x),x),y(1) = 1],y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 2.171 (sec). Leaf size: 13

DSolve[{x^2*D[y[x],x]==y[x]^2-x*y[x]*D[y[x],x],{y[1]==1}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to x W\left (\frac {e}{x}\right ) \]