Internal problem ID [506]
Book: Elementary differential equations and boundary value problems, 10th ed., Boyce and
DiPrima
Section: Section 2.2. Page 48
Problem number: 28.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {y^{\prime }-\frac {t y \left (4-y\right )}{t +1}=0} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 55
dsolve(diff(y(t),t) = t*y(t)*(4-y(t))/(1+t),y(t), singsol=all)
\[ y \left (t \right ) = \frac {4}{1+4 \,{\mathrm e}^{-4 t} c_{1} t^{4}+16 \,{\mathrm e}^{-4 t} c_{1} t^{3}+24 \,{\mathrm e}^{-4 t} c_{1} t^{2}+16 \,{\mathrm e}^{-4 t} c_{1} t +4 \,{\mathrm e}^{-4 t} c_{1}} \]
✓ Solution by Mathematica
Time used: 1.337 (sec). Leaf size: 42
DSolve[y'[t] == t*y[t]*(4-y[t])/(1+t),y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to \frac {4 e^{4 t}}{e^{4 t}+e^{4 c_1} (t+1)^4} y(t)\to 0 y(t)\to 4 \end{align*}