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 : Monday, January 27, 2025 at 01:55:51 PM
CAS classification : [_linear]

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

With initial conditions

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

✓ Solution by Maple

Time used: 0.012 (sec). Leaf size: 28

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

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

✓ Solution by Mathematica

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

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

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