Internal problem ID [11399]
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]
\[ \boxed {x^{\prime }-2 t^{3} x=-6} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 49
dsolve(diff(x(t),t)=2*t^3*x(t)-6,x(t), singsol=all)
\[ x \left (t \right ) = \frac {-\frac {24 \operatorname {WhittakerM}\left (\frac {1}{8}, \frac {5}{8}, \frac {t^{4}}{2}\right ) {\mathrm e}^{\frac {t^{4}}{4}} 2^{\frac {1}{8}} t}{5}+\left (t^{4}\right )^{\frac {1}{8}} \left ({\mathrm e}^{\frac {t^{4}}{2}} c_{1} -6 t \right )}{\left (t^{4}\right )^{\frac {1}{8}}} \]
✓ Solution by Mathematica
Time used: 0.152 (sec). Leaf size: 49
DSolve[x'[t]==2*t^3*x[t]-6,x[t],t,IncludeSingularSolutions -> True]
\[ x(t)\to \frac {1}{2} e^{\frac {t^4}{2}} \left (\frac {3 \sqrt [4]{2} t \Gamma \left (\frac {1}{4},\frac {t^4}{2}\right )}{\sqrt [4]{t^4}}+2 c_1\right ) \]