Internal problem ID [3994]
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.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_rational, _Bernoulli]
Solve \begin {gather*} \boxed {\left (-x^{3}+1\right ) y^{\prime }-2 \left (1+x \right ) y-y^{\frac {5}{2}}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.003 (sec). Leaf size: 45
dsolve((1-x^3)*diff(y(x),x)-2*(1+x)*y(x)=y(x)^(5/2),y(x), singsol=all)
\[ -\frac {c_{1}}{\frac {x^{2}}{\left (x -1\right )^{2}}+\frac {x}{\left (x -1\right )^{2}}+\frac {1}{\left (x -1\right )^{2}}}+\frac {1}{y \relax (x )^{\frac {3}{2}}}+\frac {3}{4 \left (x^{2}+x +1\right )} = 0 \]
✓ Solution by Mathematica
Time used: 1.094 (sec). Leaf size: 41
DSolve[(1-x^3)*y'[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*}