Internal problem ID [4012]
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.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class G], _rational, _Riccati]
Solve \begin {gather*} \boxed {y^{\prime }-\frac {1}{x^{2}}+\frac {y}{x}+y^{2}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.005 (sec). Leaf size: 16
dsolve(diff(y(x),x)=1/x^2-y(x)/x-y(x)^2,y(x), singsol=all)
\[ y \relax (x ) = -\frac {\tanh \left (-\ln \relax (x )+c_{1}\right )}{x} \]
✓ Solution by Mathematica
Time used: 0.409 (sec). Leaf size: 61
DSolve[y'[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*}