32.5.24 problem Exercise 11.26, page 97

Internal problem ID [5862]
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
Date solved : Monday, January 27, 2025 at 01:21:28 PM
CAS classification : [_rational, _Riccati]

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

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 17

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

\[ y \left (x \right ) = i \tan \left (-\frac {i x^{2}}{2}+c_{1} \right ) x^{2} \]

✓ Solution by Mathematica

Time used: 0.169 (sec). Leaf size: 75

DSolve[D[y[x],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*}