Internal problem ID [10381]
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).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_linear]
\[ \boxed {x^{\prime }-2 t^{3} x+6=0} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 56
dsolve(diff(x(t),t)=2*t^3*x(t)-6,x(t), singsol=all)
\[ x \left (t \right ) = {\mathrm e}^{\frac {t^{4}}{2}} c_{1} -\frac {3 \,{\mathrm e}^{\frac {t^{4}}{4}} 128^{\frac {7}{8}} \left (2 t^{4} \operatorname {WhittakerM}\left (\frac {1}{8}, \frac {5}{8}, \frac {t^{4}}{2}\right )+5 \operatorname {WhittakerM}\left (\frac {9}{8}, \frac {5}{8}, \frac {t^{4}}{2}\right )\right )}{80 t^{3} \left (t^{4}\right )^{\frac {1}{8}}} \]
✓ Solution by Mathematica
Time used: 0.097 (sec). Leaf size: 37
DSolve[x'[t]==2*t^3*x[t]-6,x[t],t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to \frac {1}{2} e^{\frac {t^4}{2}} \left (3 t \operatorname {ExpIntegralE}\left (\frac {3}{4},\frac {t^4}{2}\right )+2 c_1\right ) \\ \end{align*}