63.5.13 problem 3(a)

Internal problem ID [13016]
Book : A First Course in Differential Equations by J. David Logan. Third Edition. Springer-Verlag, NY. 2015.
Section : Chapter 1, First order differential equations. Section 1.4.1. Integrating factors. Exercises page 41
Problem number : 3(a)
Date solved : Monday, March 31, 2025 at 07:30:56 AM
CAS classification : [_linear]

\begin{align*} x^{\prime }+\frac {5 x}{t}&=1+t \end{align*}

With initial conditions

\begin{align*} x \left (1\right )&=1 \end{align*}

✓ Maple. Time used: 0.023 (sec). Leaf size: 18

ode:=diff(x(t),t)+5*x(t)/t = t+1; 
ic:=x(1) = 1; 
dsolve([ode,ic],x(t), singsol=all);
 

\[ x = \frac {t^{2}}{7}+\frac {t}{6}+\frac {29}{42 t^{5}} \]

✓ Mathematica. Time used: 0.043 (sec). Leaf size: 27

ode=D[x[t],t]+(5/t)*x[t]==1+t; 
ic={x[1]==1}; 
DSolve[{ode,ic},x[t],t,IncludeSingularSolutions->True]
 

\[ x(t)\to \frac {\int _1^t\left (K[1]^6+K[1]^5\right )dK[1]+1}{t^5} \]

✓ Sympy. Time used: 0.211 (sec). Leaf size: 17

from sympy import * 
t = symbols("t") 
x = Function("x") 
ode = Eq(-t + Derivative(x(t), t) - 1 + 5*x(t)/t,0) 
ics = {x(1): 1} 
dsolve(ode,func=x(t),ics=ics)
 

\[ x{\left (t \right )} = \frac {t^{2}}{7} + \frac {t}{6} + \frac {29}{42 t^{5}} \]