Internal problem ID [12705]
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: 20.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_linear]
\[ \boxed {y^{\prime }-t^{r} y=4} \]
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 331
dsolve(diff(y(t),t)=t^r*y(t)+4,y(t), singsol=all)
\[ y \left (t \right ) = \left (\frac {4 \left (\frac {1}{r +1}\right )^{-\frac {1}{r +1}} \left (\frac {\left (r +1\right )^{2} t^{\frac {r}{r +1}+\frac {1}{r +1}-1-r} \left (\frac {1}{r +1}\right )^{\frac {1}{r +1}} \left (\frac {t^{r +1} r^{2}}{r +1}+\frac {2 t^{r +1} r}{r +1}+r^{2}+\frac {t^{r +1}}{r +1}+3 r +2\right ) \left (\frac {t^{r +1}}{r +1}\right )^{-\frac {r +2}{2 \left (r +1\right )}} {\mathrm e}^{-\frac {t^{r +1}}{2 \left (r +1\right )}} \operatorname {WhittakerM}\left (\frac {1}{r +1}-\frac {r +2}{2 \left (r +1\right )}, \frac {r +2}{2 r +2}+\frac {1}{2}, \frac {t^{r +1}}{r +1}\right )}{\left (r +2\right ) \left (2 r +3\right )}+\frac {\left (r +1\right )^{2} t^{\frac {r}{r +1}+\frac {1}{r +1}-1-r} \left (\frac {1}{r +1}\right )^{\frac {1}{r +1}} \left (r +2\right ) \left (\frac {t^{r +1}}{r +1}\right )^{-\frac {r +2}{2 \left (r +1\right )}} {\mathrm e}^{-\frac {t^{r +1}}{2 \left (r +1\right )}} \operatorname {WhittakerM}\left (\frac {1}{r +1}-\frac {r +2}{2 \left (r +1\right )}+1, \frac {r +2}{2 r +2}+\frac {1}{2}, \frac {t^{r +1}}{r +1}\right )}{2 r +3}\right )}{r +1}+c_{1} \right ) {\mathrm e}^{\frac {t^{r +1}}{r +1}} \]
✓ Solution by Mathematica
Time used: 0.12 (sec). Leaf size: 66
DSolve[y'[t]==t^r*y[t]+4,y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to e^{\frac {t^{r+1}}{r+1}} \left (-\frac {4 t \left (\frac {t^{r+1}}{r+1}\right )^{-\frac {1}{r+1}} \Gamma \left (\frac {1}{r+1},\frac {t^{r+1}}{r+1}\right )}{r+1}+c_1\right ) \]