73.2.6 problem 3.4 f

Internal problem ID [15029]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 3. Some basics about First order equations. Additional exercises. page 63
Problem number : 3.4 f
Date solved : Tuesday, January 28, 2025 at 07:27:55 AM
CAS classification : [_quadrature]

\begin{align*} y^{3}-25 y+y^{\prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 33

dsolve(y(x)^3-25*y(x)+diff(y(x),x)=0,y(x), singsol=all)
 

\begin{align*} y &= -\frac {5}{\sqrt {25 \,{\mathrm e}^{-50 x} c_{1} +1}} \\ y &= \frac {5}{\sqrt {25 \,{\mathrm e}^{-50 x} c_{1} +1}} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.207 (sec). Leaf size: 53

DSolve[y[x]^3-25*y[x]+D[y[x],x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to \text {InverseFunction}\left [\int _1^{\text {$\#$1}}\frac {1}{(K[1]-5) K[1] (K[1]+5)}dK[1]\&\right ][-x+c_1] \\ y(x)\to -5 \\ y(x)\to 0 \\ y(x)\to 5 \\ \end{align*}