32.5.26 problem Exercise 11.28, page 97

Internal problem ID [5864]
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 11.28, page 97
Date solved : Monday, January 27, 2025 at 01:21:35 PM
CAS classification : [[_homogeneous, `class G`], _rational, _Riccati]

\begin{align*} y^{\prime }&=\frac {1}{x^{2}}-\frac {y}{x}-y^{2} \end{align*}

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 16

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

\[ y \left (x \right ) = -\frac {\tanh \left (c_{1} -\ln \left (x \right )\right )}{x} \]

✓ Solution by Mathematica

Time used: 1.208 (sec). Leaf size: 62

DSolve[D[y[x],x]==1/x^2-y[x]/x-y[x]^2,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to \frac {i \tan (c_1-i \log (x))}{x} \\ y(x)\to -\frac {-x^2+e^{2 i \text {Interval}[\{0,\pi \}]}}{x^3+x e^{2 i \text {Interval}[\{0,\pi \}]}} \\ \end{align*}