Internal problem ID [13019]
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.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_linear]
\[ \boxed {y^{\prime }-t^{2} y=4} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 41
dsolve(diff(y(t),t)=t^2*y(t)+4,y(t), singsol=all)
\[ y \left (t \right ) = \frac {3 \,3^{\frac {1}{6}} t \operatorname {WhittakerM}\left (\frac {1}{6}, \frac {2}{3}, \frac {t^{3}}{3}\right ) {\mathrm e}^{\frac {t^{3}}{6}}}{\left (t^{3}\right )^{\frac {1}{6}}}+c_{1} {\mathrm e}^{\frac {t^{3}}{3}}+4 t \]
✓ Solution by Mathematica
Time used: 0.102 (sec). Leaf size: 49
DSolve[y'[t]==t^2*y[t]+4,y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to \frac {1}{3} e^{\frac {t^3}{3}} \left (-\frac {4 \sqrt [3]{3} t \Gamma \left (\frac {1}{3},\frac {t^3}{3}\right )}{\sqrt [3]{t^3}}+3 c_1\right ) \]