57.5.1 problem 1(a)

Internal problem ID [14356]
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 : 1(a)
Date solved : Thursday, October 02, 2025 at 09:32:22 AM
CAS classification : [_linear]

\begin{align*} x^{\prime }&=2 t^{3} x-6 \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 50

ode:=diff(x(t),t) = 2*t^3*x(t)-6; 
dsolve(ode,x(t), singsol=all);
 

\[ x = -\frac {24 \left (\operatorname {WhittakerM}\left (\frac {1}{8}, \frac {5}{8}, \frac {t^{4}}{2}\right ) {\mathrm e}^{\frac {t^{4}}{4}} 2^{{1}/{8}} t -\frac {5 \left ({\mathrm e}^{\frac {t^{4}}{2}} c_1 -6 t \right ) \left (t^{4}\right )^{{1}/{8}}}{24}\right )}{5 \left (t^{4}\right )^{{1}/{8}}} \]

✓ Mathematica. Time used: 0.05 (sec). Leaf size: 49

ode=D[x[t],t]==2*t^3*x[t]-6; 
ic={}; 
DSolve[{ode,ic},x[t],t,IncludeSingularSolutions->True]
 

\begin{align*} x(t)&\to \frac {1}{2} e^{\frac {t^4}{2}} \left (\frac {3 \sqrt [4]{2} t \Gamma \left (\frac {1}{4},\frac {t^4}{2}\right )}{\sqrt [4]{t^4}}+2 c_1\right ) \end{align*}

✓ Sympy. Time used: 0.475 (sec). Leaf size: 27

from sympy import * 
t = symbols("t") 
x = Function("x") 
ode = Eq(-2*t**3*x(t) + Derivative(x(t), t) + 6,0) 
ics = {} 
dsolve(ode,func=x(t),ics=ics)
 

\[ x{\left (t \right )} = \left (C_{1} - \frac {3 \sqrt [4]{2} \gamma \left (\frac {1}{4}, \frac {t^{4}}{2}\right )}{2}\right ) e^{\frac {t^{4}}{2}} \]