Internal problem ID [4612]
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.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class A`], _rational, [_Abel, `2nd type`, `class B`]]
\[ \boxed {x^{2} y^{\prime }-y^{2}+x y y^{\prime }=0} \] With initial conditions \begin {align*} [y \left (1\right ) = 1] \end {align*}
✓ Solution by Maple
Time used: 0.187 (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)
\[ y \left (x \right ) = \operatorname {LambertW}\left (\frac {{\mathrm e}}{x}\right ) x \]
✓ Solution by Mathematica
Time used: 2.205 (sec). Leaf size: 13
DSolve[{x^2*y'[x]==y[x]^2-x*y[x]*y'[x],{y[1]==1}},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to x W\left (\frac {e}{x}\right ) \\ \end{align*}