Internal problem ID [4444]
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.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_linear]
\[ \boxed {3 t -{\mathrm e}^{t} y^{\prime }-y \ln \left (t \right )=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 41
dsolve(3*t=exp(t)*diff(y(t),t)+y(t)*ln(t),y(t), singsol=all)
\[ y \left (t \right ) = \left (\int 3 t^{1-{\mathrm e}^{-t}} {\mathrm e}^{-t -\operatorname {Ei}_{1}\left (t \right )}d t +c_{1} \right ) t^{{\mathrm e}^{-t}} {\mathrm e}^{\operatorname {Ei}_{1}\left (t \right )} \]
✓ Solution by Mathematica
Time used: 0.233 (sec). Leaf size: 58
DSolve[3*t==Exp[t]*y'[t]+y[t]*Log[t],y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to t^{e^{-t}} e^{-\operatorname {ExpIntegralEi}(-t)} \left (\int _1^t3 e^{\operatorname {ExpIntegralEi}(-K[1])-K[1]} K[1]^{-\cosh (K[1])+\sinh (K[1])+1}dK[1]+c_1\right ) \\ \end{align*}