72.7.20 problem 20

Internal problem ID [14682]
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
Date solved : Thursday, March 13, 2025 at 04:14:20 AM
CAS classification : [_linear]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 202

ode:=diff(y(t),t) = t^r*y(t)+4; 
dsolve(ode,y(t), singsol=all);
 

\[ y = \frac {4 \left (\left (\frac {t \,t^{r}}{r +1}\right )^{\frac {-r -2}{2 r +2}} t^{-r} \left (r +1\right ) \left (r +2\right )^{2} \operatorname {WhittakerM}\left (\frac {r +2}{2 r +2}, \frac {2 r +3}{2 r +2}, \frac {t \,t^{r}}{r +1}\right )+\left (\left (r +2\right ) t^{-r}+t \right ) \left (r +1\right )^{2} \left (\frac {t \,t^{r}}{r +1}\right )^{\frac {-r -2}{2 r +2}} \operatorname {WhittakerM}\left (-\frac {r}{2 r +2}, \frac {2 r +3}{2 r +2}, \frac {t \,t^{r}}{r +1}\right )+\frac {c_{1} \left (r +2\right ) \left (r +\frac {3}{2}\right ) {\mathrm e}^{\frac {t^{r} t}{2 r +2}}}{2}\right ) {\mathrm e}^{\frac {t^{r} t}{2 r +2}}}{2 r^{2}+7 r +6} \]

✓ Mathematica. Time used: 0.065 (sec). Leaf size: 66

ode=D[y[t],t]==t^r*y[t]+4; 
ic={}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

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

✗ Sympy

from sympy import * 
t = symbols("t") 
r = symbols("r") 
y = Function("y") 
ode = Eq(-t**r*y(t) + Derivative(y(t), t) - 4,0) 
ics = {} 
dsolve(ode,func=y(t),ics=ics)
 

Timed Out