38.1.11 problem 11

Internal problem ID [6428]
Book : Engineering Mathematics. By K. A. Stroud. 5th edition. Industrial press Inc. NY. 2001
Section : Program 24. First order differential equations. Test excercise 24. page 1067
Problem number : 11
Date solved : Monday, January 27, 2025 at 02:02:40 PM
CAS classification : [[_homogeneous, `class G`], _rational, _Bernoulli]

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

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 27

dsolve(diff(y(x),x)+y(x)/x=y(x)^3,y(x), singsol=all)
 

\begin{align*} y &= \frac {1}{\sqrt {x \left (c_1 x +2\right )}} \\ y &= -\frac {1}{\sqrt {x \left (c_1 x +2\right )}} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.468 (sec). Leaf size: 40

DSolve[D[y[x],x]+y[x]/x==y[x]^3,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to -\frac {1}{\sqrt {x (2+c_1 x)}} \\ y(x)\to \frac {1}{\sqrt {x (2+c_1 x)}} \\ y(x)\to 0 \\ \end{align*}