Internal problem ID [4010]
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 11.26, page 97.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_rational, _Riccati]
Solve \begin {gather*} \boxed {y^{\prime }-x^{3}-\frac {2 y}{x}+\frac {y^{2}}{x}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 19
dsolve(diff(y(x),x)=x^3+2/x*y(x)-1/x*y(x)^2,y(x), singsol=all)
\[ y \relax (x ) = i \tan \left (-\frac {i x^{2}}{2}+c_{1}\right ) x^{2} \]
✓ Solution by Mathematica
Time used: 0.257 (sec). Leaf size: 75
DSolve[y'[x]==x^3+2/x*y[x]-1/x*y[x]^2,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {x^2 \left (i \cosh \left (\frac {x^2}{2}\right )+c_1 \sinh \left (\frac {x^2}{2}\right )\right )}{i \sinh \left (\frac {x^2}{2}\right )+c_1 \cosh \left (\frac {x^2}{2}\right )} \\ y(x)\to x^2 \tanh \left (\frac {x^2}{2}\right ) \\ \end{align*}