63.5.1 problem 1(a)

Internal problem ID [13075]
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 : Tuesday, January 28, 2025 at 04:51:29 AM
CAS classification : [_linear]

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 50

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

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

✓ Solution by Mathematica

Time used: 0.086 (sec). Leaf size: 49

DSolve[D[x[t],t]==2*t^3*x[t]-6,x[t],t,IncludeSingularSolutions -> True]
 

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