73.7.13 problem 13

Internal problem ID [15171]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 8. Review exercises for part of part II. page 143
Problem number : 13
Date solved : Tuesday, January 28, 2025 at 07:39:56 AM
CAS classification : [[_homogeneous, `class D`], _rational, _Bernoulli]

\begin{align*} 3 x y^{3}-y+x y^{\prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 30

dsolve(3*x*y(x)^3-y(x)+x*diff(y(x),x)=0,y(x), singsol=all)
 

\begin{align*} y &= \frac {x}{\sqrt {2 x^{3}+c_{1}}} \\ y &= -\frac {x}{\sqrt {2 x^{3}+c_{1}}} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.207 (sec). Leaf size: 43

DSolve[3*x*y[x]^3-y[x]+x*D[y[x],x]==0,y[x],x,IncludeSingularSolutions -> True]
 

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