36.2.4 problem 4

Internal problem ID [6297]
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 : 4
Date solved : Monday, January 27, 2025 at 01:55:17 PM
CAS classification : [_linear]

\begin{align*} 3 t&={\mathrm e}^{t} y^{\prime }+y \ln \left (t \right ) \end{align*}

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 42

dsolve(3*t=exp(t)*diff(y(t),t)+y(t)*ln(t),y(t), singsol=all)
 

\[ y = \left (3 \left (\int t^{1-{\mathrm e}^{-t}} {\mathrm e}^{-t -\operatorname {Ei}_{1}\left (t \right )}d t \right )+c_{1} \right ) t^{{\mathrm e}^{-t}} {\mathrm e}^{\operatorname {Ei}_{1}\left (t \right )} \]

✓ Solution by Mathematica

Time used: 0.257 (sec). Leaf size: 58

DSolve[3*t==Exp[t]*D[y[t],t]+y[t]*Log[t],y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to t^{e^{-t}} e^{-\operatorname {ExpIntegralEi}(-t)} \left (\int _1^t3 e^{\operatorname {ExpIntegralEi}(-K[1])-K[1]} K[1]^{1-e^{-K[1]}}dK[1]+c_1\right ) \]