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 3.11.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {y^{\prime }+\frac {2}{t}-\frac {y}{t}-\frac {y^{2}}{t}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.07 (sec). Leaf size: 23
dsolve(diff(y(t),t)=-2/t+1/t*y(t)+1/t*y(t)^2,y(t), singsol=all)
\[ y \relax (t ) = -\frac {2 c_{1} t^{3}+1}{c_{1} t^{3}-1} \]
✓ Solution by Mathematica
Time used: 0.486 (sec). Leaf size: 43
DSolve[y'[t]==-2/t+1/t*y[t]+1/t*y[t]^2,y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to \frac {1-2 e^{3 c_1} t^3}{1+e^{3 c_1} t^3} \\ y(t)\to -2 \\ y(t)\to 1 \\ \end{align*}