17.2.6 problem 1.1-3 (f)

Internal problem ID [3430]
Book : Ordinary Differential Equations, Robert H. Martin, 1983
Section : Problem 1.1-3, page 6
Problem number : 1.1-3 (f)
Date solved : Tuesday, March 04, 2025 at 04:38:32 PM
CAS classification : [_quadrature]

\begin{align*} y^{\prime }&=8 \,{\mathrm e}^{4 t}+t \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=12 \end{align*}

✓ Maple. Time used: 0.009 (sec). Leaf size: 17

ode:=diff(y(t),t) = 8*exp(4*t)+t; 
ic:=y(0) = 12; 
dsolve([ode,ic],y(t), singsol=all);
 

\[ y = \frac {t^{2}}{2}+2 \,{\mathrm e}^{4 t}+10 \]

✓ Mathematica. Time used: 0.009 (sec). Leaf size: 21

ode=D[y[t],t]==8*Exp[4*t]+t; 
ic=y[0]==12; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\[ y(t)\to \frac {1}{2} \left (t^2+4 e^{4 t}+20\right ) \]

✓ Sympy. Time used: 0.140 (sec). Leaf size: 15

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(-t - 8*exp(4*t) + Derivative(y(t), t),0) 
ics = {y(0): 12} 
dsolve(ode,func=y(t),ics=ics)
 

\[ y{\left (t \right )} = \frac {t^{2}}{2} + 2 e^{4 t} + 10 \]