86.3.15 problem 13

Internal problem ID [23106]
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 4a at page 56
Problem number : 13
Date solved : Thursday, October 02, 2025 at 09:22:02 PM
CAS classification : [_quadrature]

\begin{align*} p^{\prime }&=15-20 p \end{align*}

With initial conditions

\begin{align*} p \left (0\right )&={\frac {7}{10}} \\ \end{align*}

✓ Maple. Time used: 0.008 (sec). Leaf size: 12

ode:=diff(p(t),t) = 15-20*p(t); 
ic:=[p(0) = 7/10]; 
dsolve([ode,op(ic)],p(t), singsol=all);
 

\[ p = \frac {3}{4}-\frac {{\mathrm e}^{-20 t}}{20} \]

✓ Mathematica. Time used: 0.03 (sec). Leaf size: 18

ode=D[p[t],t]==15-20*p[t]; 
ic={p[0]==7/10}; 
DSolve[{ode,ic},p[t],t,IncludeSingularSolutions->True]
 

\begin{align*} p(t)&\to \frac {3}{4}-\frac {e^{-20 t}}{20} \end{align*}

✓ Sympy. Time used: 0.106 (sec). Leaf size: 27

from sympy import * 
t = symbols("t") 
p = Function("p") 
ode = Eq(x*y(x) + 20*p(t) + Derivative(p(t), t) - 15,0) 
ics = {p(0): 7/10} 
dsolve(ode,func=p(t),ics=ics)
 

\[ p{\left (t \right )} = - \frac {x y{\left (x \right )}}{20} + \left (\frac {x y{\left (x \right )}}{20} - \frac {1}{20}\right ) e^{- 20 t} + \frac {3}{4} \]