Internal problem ID [5091]
Book: THEORY OF DIFFERENTIAL EQUATIONS IN ENGINEERING AND MECHANICS. K.T.
CHAU, CRC Press. Boca Raton, FL. 2018
Section: Chapter 3. Ordinary Differential Equations. Section 3.2 FIRST ORDER ODE. Page
114
Problem number: Example 3.12.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_rational, _Riccati]
\[ \boxed {y^{\prime }+\frac {y}{t}+1+y^{2}=0} \]
✓ Solution by Maple
Time used: 0.047 (sec). Leaf size: 36
dsolve(diff(y(t),t)=-y(t)/t-1-y(t)^2,y(t), singsol=all)
\[ y \left (t \right ) = \frac {2 \operatorname {BesselK}\left (1, i t \right ) c_{1} -\operatorname {BesselJ}\left (1, t\right )}{2 i \operatorname {BesselK}\left (0, i t \right ) c_{1} +\operatorname {BesselJ}\left (0, t\right )} \]
✓ Solution by Mathematica
Time used: 0.185 (sec). Leaf size: 43
DSolve[y'[t]==-y[t]/t-1-y[t]^2,y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to -\frac {Y_1(t)+c_1 \operatorname {BesselJ}(1,t)}{Y_0(t)+c_1 \operatorname {BesselJ}(0,t)} \\ y(t)\to -\frac {\operatorname {BesselJ}(1,t)}{\operatorname {BesselJ}(0,t)} \\ \end{align*}