72.7.14 problem 14

Internal problem ID [14676]
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 : Thursday, March 13, 2025 at 04:13:42 AM
CAS classification : [_linear]

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

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

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

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

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

ode=D[y[t],t]==t^2*y[t]+4; 
ic={}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

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

✓ Sympy. Time used: 0.702 (sec). Leaf size: 27

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(-t**2*y(t) + Derivative(y(t), t) - 4,0) 
ics = {} 
dsolve(ode,func=y(t),ics=ics)
 

\[ y{\left (t \right )} = \left (C_{1} + \frac {4 \sqrt [3]{3} \gamma \left (\frac {1}{3}, \frac {t^{3}}{3}\right )}{3}\right ) e^{\frac {t^{3}}{3}} \]