Internal problem ID [5092]
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]
Solve \begin {gather*} \boxed {y^{\prime }+\frac {y}{t}+1+y^{2}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.108 (sec). Leaf size: 36
dsolve(diff(y(t),t)=-y(t)/t-1-y(t)^2,y(t), singsol=all)
\[ y \relax (t ) = \frac {2 \BesselK \left (1, i t \right ) c_{1}-\BesselJ \left (1, t\right )}{2 i \BesselK \left (0, i t \right ) c_{1}+\BesselJ \left (0, t\right )} \]
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 60
DSolve[y'[x]==-y[t]/t-1-y[t]^2,y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to -\frac {t \sqrt {\frac {1}{t^2}-4 y'(x)-4}+1}{2 t} \\ y(t)\to \frac {1}{2} \left (\sqrt {\frac {1}{t^2}-4 y'(x)-4}-\frac {1}{t}\right ) \\ \end{align*}