48.1.12 problem Example 3.12

Internal problem ID [7513]
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
Date solved : Monday, January 27, 2025 at 03:03:19 PM
CAS classification : [_rational, _Riccati]

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

✓ Solution by Maple

Time used: 0.060 (sec). Leaf size: 32

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

\[ y = \frac {-i \operatorname {BesselK}\left (1, i t \right ) c_{1} -\operatorname {BesselJ}\left (1, t\right )}{\operatorname {BesselK}\left (0, i t \right ) c_{1} +\operatorname {BesselJ}\left (0, t\right )} \]

✓ Solution by Mathematica

Time used: 0.176 (sec). Leaf size: 43

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

\begin{align*} y(t)\to -\frac {\operatorname {BesselY}(1,t)+c_1 \operatorname {BesselJ}(1,t)}{\operatorname {BesselY}(0,t)+c_1 \operatorname {BesselJ}(0,t)} \\ y(t)\to -\frac {\operatorname {BesselJ}(1,t)}{\operatorname {BesselJ}(0,t)} \\ \end{align*}