Internal problem ID [4579]
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: 1.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {x \left (y-3\right ) y^{\prime }-4 y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.047 (sec). Leaf size: 25
dsolve(x*(y(x)-3)*diff(y(x),x)=4*y(x),y(x), singsol=all)
\[ y \relax (x ) = {\mathrm e}^{-\LambertW \left (-\frac {{\mathrm e}^{-\frac {4 c_{1}}{3}}}{3 x^{\frac {4}{3}}}\right )-\frac {4 \ln \relax (x )}{3}-\frac {4 c_{1}}{3}} \]
✓ Solution by Mathematica
Time used: 60.144 (sec). Leaf size: 89
DSolve[x*(y[x]-3)*y'[x]==4*y[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -3 \text {ProductLog}\left (\frac {1}{3} \sqrt [3]{-\frac {e^{-c_1}}{x^4}}\right ) \\ y(x)\to -3 \text {ProductLog}\left (-\frac {1}{3} \sqrt [3]{-1} \sqrt [3]{-\frac {e^{-c_1}}{x^4}}\right ) \\ y(x)\to -3 \text {ProductLog}\left (\frac {1}{3} (-1)^{2/3} \sqrt [3]{-\frac {e^{-c_1}}{x^4}}\right ) \\ \end{align*}