Internal problem ID [4613]
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]]
Solve \begin {gather*} \boxed {y^{\prime } x^{2}-y^{2}+x y y^{\prime }=0} \end {gather*} With initial conditions \begin {align*} [y \relax (1) = 1] \end {align*}
✓ Solution by Maple
Time used: 0.578 (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)
\[ y \relax (x ) = \LambertW \left (\frac {{\mathrm e}}{x}\right ) x \]
✓ Solution by Mathematica
Time used: 9.211 (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 \text {ProductLog}\left (\frac {e}{x}\right ) \\ \end{align*}