2.4 problem 4

Internal problem ID [4445]

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]

Solve \begin {gather*} \boxed {3 t -{\mathrm e}^{t} y^{\prime }-\ln \relax (t ) y=0} \end {gather*}

Solution by Maple

Time used: 0.047 (sec). Leaf size: 41

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

\[ y \relax (t ) = \left (\int 3 t^{1-{\mathrm e}^{-t}} {\mathrm e}^{-t -\expIntegral \left (1, t\right )}d t +c_{1}\right ) t^{{\mathrm e}^{-t}} {\mathrm e}^{\expIntegral \left (1, t\right )} \]

Solution by Mathematica

Time used: 0.347 (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^{-\text {Ei}(-t)} \left (\int _1^t3 e^{\text {Ei}(-K[1])-K[1]} K[1]^{-\cosh (K[1])+\sinh (K[1])+1}dK[1]+c_1\right ) \\ \end{align*}