73.5.10 problem 6.5 (b)

Internal problem ID [15121]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 6. Simplifying through simplifiction. Additional exercises. page 114
Problem number : 6.5 (b)
Date solved : Tuesday, January 28, 2025 at 07:33:53 AM
CAS classification : [[_homogeneous, `class A`], _rational, _Bernoulli]

\begin{align*} y^{\prime }-\frac {3 y}{x}&=\frac {y^{2}}{x^{2}} \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 18

dsolve(diff(y(x),x)-3*y(x)/x=(y(x)/x)^2,y(x), singsol=all)
 

\[ y = -\frac {2 x^{3}}{x^{2}-2 c_{1}} \]

✓ Solution by Mathematica

Time used: 0.145 (sec). Leaf size: 25

DSolve[D[y[x],x]-3*y[x]/x==(y[x]/x)^2,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to -\frac {2 x^3}{x^2-2 c_1} \\ y(x)\to 0 \\ \end{align*}