Internal problem ID [529]
Book: Elementary differential equations and boundary value problems, 10th ed., Boyce and
DiPrima
Section: Section 2.4. Page 76
Problem number: 18.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_Bernoulli]
Solve \begin {gather*} \boxed {y^{\prime }-y \left (3-y t \right )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 20
dsolve(diff(y(t),t) = y(t)*(3-t*y(t)),y(t), singsol=all)
\[ y \relax (t ) = \frac {9}{-1+9 c_{1} {\mathrm e}^{-3 t}+3 t} \]
✓ Solution by Mathematica
Time used: 0.13 (sec). Leaf size: 29
DSolve[y'[t] == y[t]*(3-t*y[t]),y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to \frac {1}{\frac {t}{3}+c_1 e^{-3 t}-\frac {1}{9}} \\ y(t)\to 0 \\ \end{align*}