72.7.14 problem 14

Internal problem ID [14755]
Book : DIFFERENTIAL EQUATIONS by Paul Blanchard, Robert L. Devaney, Glen R. Hall. 4th edition. Brooks/Cole. Boston, USA. 2012
Section : Chapter 1. First-Order Differential Equations. Exercises section 1.9 page 133
Problem number : 14
Date solved : Tuesday, January 28, 2025 at 07:13:53 AM
CAS classification : [_linear]

\begin{align*} y^{\prime }&=t^{2} y+4 \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 41

dsolve(diff(y(t),t)=t^2*y(t)+4,y(t), singsol=all)
 

\[ y = \frac {3 \,3^{{1}/{6}} t \operatorname {WhittakerM}\left (\frac {1}{6}, \frac {2}{3}, \frac {t^{3}}{3}\right ) {\mathrm e}^{\frac {t^{3}}{6}}}{\left (t^{3}\right )^{{1}/{6}}}+c_{1} {\mathrm e}^{\frac {t^{3}}{3}}+4 t \]

✓ Solution by Mathematica

Time used: 0.076 (sec). Leaf size: 49

DSolve[D[y[t],t]==t^2*y[t]+4,y[t],t,IncludeSingularSolutions -> True]
 

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