Internal problem ID [13025]
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: 0.0 (sec). Leaf size: 202
dsolve(diff(y(t),t)=t^r*y(t)+4,y(t), singsol=all)
\[ y \left (t \right ) = \frac {4 \,{\mathrm e}^{\frac {t^{r} t}{2 r +2}} \left (t^{-r} \left (\frac {t \,t^{r}}{r +1}\right )^{\frac {-r -2}{2 r +2}} \left (r +1\right ) \left (r +2\right )^{2} \operatorname {WhittakerM}\left (\frac {r +2}{2 r +2}, \frac {2 r +3}{2 r +2}, \frac {t \,t^{r}}{r +1}\right )+\left (r +1\right )^{2} \left (\left (r +2\right ) t^{-r}+t \right ) \left (\frac {t \,t^{r}}{r +1}\right )^{\frac {-r -2}{2 r +2}} \operatorname {WhittakerM}\left (-\frac {r}{2 r +2}, \frac {2 r +3}{2 r +2}, \frac {t \,t^{r}}{r +1}\right )+\frac {\left (r +\frac {3}{2}\right ) c_{1} \left (r +2\right ) {\mathrm e}^{\frac {t^{r} t}{2 r +2}}}{2}\right )}{2 r^{2}+7 r +6} \]
✓ Solution by Mathematica
Time used: 0.12 (sec). Leaf size: 66
DSolve[y'[t]==t^r*y[t]+4,y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to e^{\frac {t^{r+1}}{r+1}} \left (-\frac {4 t \left (\frac {t^{r+1}}{r+1}\right )^{-\frac {1}{r+1}} \Gamma \left (\frac {1}{r+1},\frac {t^{r+1}}{r+1}\right )}{r+1}+c_1\right ) \]