86.4.7 problem 6 (b)

Internal problem ID [23114]
Book : An introduction to Differential Equations. By Howard Frederick Cleaves. 1969. Oliver and Boyd publisher. ISBN 0050015044
Section : Chapter 4. Linear equations of the first order. Exercise 4b at page 64
Problem number : 6 (b)
Date solved : Thursday, October 02, 2025 at 09:23:01 PM
CAS classification : [[_linear, `class A`]]

\begin{align*} v^{\prime }&=60 t -4 v \end{align*}

With initial conditions

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

✓ Maple. Time used: 0.008 (sec). Leaf size: 15

ode:=diff(v(t),t) = 60*t-4*v(t); 
ic:=[v(0) = 0]; 
dsolve([ode,op(ic)],v(t), singsol=all);
 

\[ v = 15 t -\frac {15}{4}+\frac {15 \,{\mathrm e}^{-4 t}}{4} \]

✓ Mathematica. Time used: 0.032 (sec). Leaf size: 19

ode=D[v[t],t]==60*t-4*v[t]; 
ic={v[0]==0}; 
DSolve[{ode,ic},v[t],t,IncludeSingularSolutions->True]
 

\begin{align*} v(t)&\to \frac {15}{4} \left (4 t+e^{-4 t}-1\right ) \end{align*}

✓ Sympy. Time used: 0.081 (sec). Leaf size: 17

from sympy import * 
t = symbols("t") 
v = Function("v") 
ode = Eq(-60*t + 4*v(t) + Derivative(v(t), t),0) 
ics = {v(0): 0} 
dsolve(ode,func=v(t),ics=ics)
 

\[ v{\left (t \right )} = 15 t - \frac {15}{4} + \frac {15 e^{- 4 t}}{4} \]