Internal problem ID [11439]
Book: A First Course in Differential Equations by J. David Logan. Third Edition. Springer-Verlag,
NY. 2015.
Section: Chapter 1, First order differential equations. Section 1.4.1. Integrating factors. Exercises
page 41
Problem number: 15(f).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_Bernoulli]
\[ \boxed {w^{\prime }-w t -t^{3} w^{3}=0} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 43
dsolve(diff(w(t),t)=t*w(t)+t^3*w(t)^3,w(t), singsol=all)
\begin{align*} w \left (t \right ) = \frac {1}{\sqrt {{\mathrm e}^{-t^{2}} c_{1} -t^{2}+1}} w \left (t \right ) = -\frac {1}{\sqrt {{\mathrm e}^{-t^{2}} c_{1} -t^{2}+1}} \end{align*}
✓ Solution by Mathematica
Time used: 2.07 (sec). Leaf size: 80
DSolve[w'[t]==t*w[t]+t^3*w[t]^3,w[t],t,IncludeSingularSolutions -> True]
\begin{align*} w(t)\to -\frac {i e^{\frac {t^2}{2}}}{\sqrt {e^{t^2} \left (t^2-1\right )-c_1}} w(t)\to \frac {i e^{\frac {t^2}{2}}}{\sqrt {e^{t^2} \left (t^2-1\right )-c_1}} w(t)\to 0 \end{align*}