Internal problem ID [14426]
Book: INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton.
Fourth edition 2014. ElScAe. 2014
Section: Chapter 2. First Order Equations. Review exercises, page 80
Problem number: 24.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_Bernoulli]
\[ \boxed {y^{\prime }-y-y^{3} t=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 39
dsolve(diff(y(t),t)-y(t)=t*y(t)^3,y(t), singsol=all)
\begin{align*} y \left (t \right ) &= -\frac {2}{\sqrt {2+4 \,{\mathrm e}^{-2 t} c_{1} -4 t}} \\ y \left (t \right ) &= \frac {2}{\sqrt {2+4 \,{\mathrm e}^{-2 t} c_{1} -4 t}} \\ \end{align*}
✓ Solution by Mathematica
Time used: 1.817 (sec). Leaf size: 68
DSolve[y'[t]-y[t]==t*y[t]^3,y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to -\frac {i e^t}{\sqrt {e^{2 t} \left (t-\frac {1}{2}\right )-c_1}} \\ y(t)\to \frac {i e^t}{\sqrt {e^{2 t} \left (t-\frac {1}{2}\right )-c_1}} \\ y(t)\to 0 \\ \end{align*}