57.5.31 problem 15(f)

Internal problem ID [14386]
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 : Thursday, October 02, 2025 at 09:36:06 AM
CAS classification : [_Bernoulli]

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

✓ Maple. Time used: 0.004 (sec). Leaf size: 43

ode:=diff(w(t),t) = t*w(t)+t^3*w(t)^3; 
dsolve(ode,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*}

✓ Mathematica. Time used: 1.79 (sec). Leaf size: 80

ode=D[w[t],t]==t*w[t]+t^3*w[t]^3; 
ic={}; 
DSolve[{ode,ic},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*}

✓ Sympy. Time used: 0.550 (sec). Leaf size: 53

from sympy import * 
t = symbols("t") 
w = Function("w") 
ode = Eq(-t**3*w(t)**3 - t*w(t) + Derivative(w(t), t),0) 
ics = {} 
dsolve(ode,func=w(t),ics=ics)
 

\[ \left [ w{\left (t \right )} = - \sqrt {\frac {e^{t^{2}}}{C_{1} - t^{2} e^{t^{2}} + e^{t^{2}}}}, \ w{\left (t \right )} = \sqrt {\frac {e^{t^{2}}}{C_{1} - t^{2} e^{t^{2}} + e^{t^{2}}}}\right ] \]