63.5.31 problem 15(f)

Internal problem ID [13105]
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)
Date solved : Tuesday, January 28, 2025 at 04:52:33 AM
CAS classification : [_Bernoulli]

\begin{align*} w^{\prime }&=t w+t^{3} w^{3} \end{align*}

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 43

dsolve(diff(w(t),t)=t*w(t)+t^3*w(t)^3,w(t), singsol=all)
 

\begin{align*} w &= \frac {1}{\sqrt {{\mathrm e}^{-t^{2}} c_{1} -t^{2}+1}} \\ w &= -\frac {1}{\sqrt {{\mathrm e}^{-t^{2}} c_{1} -t^{2}+1}} \\ \end{align*}

✓ Solution by Mathematica

Time used: 1.877 (sec). Leaf size: 80

DSolve[D[w[t],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*}