32.5.8 problem Exercise 11.8, page 97

Internal problem ID [5846]
Book : Ordinary Differential Equations, By Tenenbaum and Pollard. Dover, NY 1963
Section : Chapter 2. Special types of differential equations of the first kind. Lesson 11, Bernoulli Equations
Problem number : Exercise 11.8, page 97
Date solved : Monday, January 27, 2025 at 01:20:30 PM
CAS classification : [_rational, _Bernoulli]

\begin{align*} \left (-x^{3}+1\right ) y^{\prime }-2 \left (1+x \right ) y&=y^{{5}/{2}} \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 38

dsolve((1-x^3)*diff(y(x),x)-2*(1+x)*y(x)=y(x)^(5/2),y(x), singsol=all)
 

\[ -\frac {\left (x -1\right )^{2} c_{1}}{x^{2}+x +1}+\frac {1}{y \left (x \right )^{{3}/{2}}}+\frac {3}{4 x^{2}+4 x +4} = 0 \]

✓ Solution by Mathematica

Time used: 4.153 (sec). Leaf size: 41

DSolve[(1-x^3)*D[y[x],x]-2*(1+x)*y[x]==y[x]^(5/2),y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to \frac {2 \sqrt [3]{2}}{\left (\frac {-3+4 c_1 (x-1)^2}{x^2+x+1}\right ){}^{2/3}} \\ y(x)\to 0 \\ \end{align*}