38.2.1 problem 1

Internal problem ID [6430]
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
Date solved : Monday, January 27, 2025 at 02:02:46 PM
CAS classification : [_separable]

\begin{align*} x \left (y-3\right ) y^{\prime }&=4 y \end{align*}

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 16

dsolve(x*(y(x)-3)*diff(y(x),x)=4*y(x),y(x), singsol=all)
 

\[ y = -3 \operatorname {LambertW}\left (-\frac {{\mathrm e}^{-\frac {4 c_1}{3}}}{3 x^{{4}/{3}}}\right ) \]

✓ Solution by Mathematica

Time used: 11.828 (sec). Leaf size: 94

DSolve[x*(y[x]-3)*D[y[x],x]==4*y[x],y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to -3 W\left (\frac {1}{3} \sqrt [3]{-\frac {e^{-c_1}}{x^4}}\right ) \\ y(x)\to -3 W\left (-\frac {1}{3} \sqrt [3]{-1} \sqrt [3]{-\frac {e^{-c_1}}{x^4}}\right ) \\ y(x)\to -3 W\left (\frac {1}{3} (-1)^{2/3} \sqrt [3]{-\frac {e^{-c_1}}{x^4}}\right ) \\ y(x)\to 0 \\ \end{align*}