72.6.6 problem 6

Internal problem ID [14660]
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 1.8 page 121
Problem number : 6
Date solved : Monday, March 31, 2025 at 12:51:49 PM
CAS classification : [[_linear, `class A`]]

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

✓ Maple. Time used: 0.001 (sec). Leaf size: 14

ode:=diff(y(t),t) = 1/2*y(t)+4*exp(1/2*t); 
dsolve(ode,y(t), singsol=all);
 

\[ y = \left (4 t +c_1 \right ) {\mathrm e}^{\frac {t}{2}} \]

✓ Mathematica. Time used: 0.041 (sec). Leaf size: 19

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

\[ y(t)\to e^{t/2} (4 t+c_1) \]

✓ Sympy. Time used: 0.152 (sec). Leaf size: 12

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

\[ y{\left (t \right )} = \left (C_{1} + 4 t\right ) e^{\frac {t}{2}} \]