73.3.37 problem 4.7 (k)

Internal problem ID [15071]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 4. SEPARABLE FIRST ORDER EQUATIONS. Additional exercises. page 90
Problem number : 4.7 (k)
Date solved : Tuesday, January 28, 2025 at 07:29:38 AM
CAS classification : [_separable]

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 27

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

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

✓ Solution by Mathematica

Time used: 0.171 (sec). Leaf size: 44

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

\begin{align*} y(x)\to -\frac {1}{\sqrt {-3 x^2-2 c_1}} \\ y(x)\to \frac {1}{\sqrt {-3 x^2-2 c_1}} \\ y(x)\to 0 \\ \end{align*}