36.2.19 problem 19

Internal problem ID [6312]
Book : Fundamentals of Differential Equations. By Nagle, Saff and Snider. 9th edition. Boston. Pearson 2018.
Section : Chapter 2, First order differential equations. Section 2.3, Linear equations. Exercises. page 54
Problem number : 19
Date solved : Sunday, March 30, 2025 at 10:50:30 AM
CAS classification : [_linear]

\begin{align*} t^{2} x^{\prime }+3 t x&=t^{4} \ln \left (t \right )+1 \end{align*}

With initial conditions

\begin{align*} x \left (1\right )&=0 \end{align*}

✓ Maple. Time used: 0.023 (sec). Leaf size: 28

ode:=t^2*diff(x(t),t)+3*x(t)*t = t^4*ln(t)+1; 
ic:=x(1) = 0; 
dsolve([ode,ic],x(t), singsol=all);
 

\[ x = \frac {6 t^{6} \ln \left (t \right )-t^{6}+18 t^{2}-17}{36 t^{3}} \]

✓ Mathematica. Time used: 0.041 (sec). Leaf size: 29

ode=t^2*D[x[t],t]+3*t*x[t]==t^4*Log[t]+1; 
ic={x[1]==0}; 
DSolve[{ode,ic},x[t],t,IncludeSingularSolutions->True]
 

\[ x(t)\to -\frac {t^6-6 t^6 \log (t)-18 t^2+17}{36 t^3} \]

✓ Sympy. Time used: 0.284 (sec). Leaf size: 26

from sympy import * 
t = symbols("t") 
x = Function("x") 
ode = Eq(-t**4*log(t) + t**2*Derivative(x(t), t) + 3*t*x(t) - 1,0) 
ics = {x(1): 0} 
dsolve(ode,func=x(t),ics=ics)
 

\[ x{\left (t \right )} = \frac {\frac {t^{6} \left (6 \log {\left (t \right )} - 1\right )}{36} + \frac {t^{2}}{2} - \frac {17}{36}}{t^{3}} \]