Internal problem ID [4953]
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]
\[ \boxed {-{\mathrm e}^{t} y^{\prime }-y \ln \left (t \right )=-3 t} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 42
dsolve(3*t=exp(t)*diff(y(t),t)+y(t)*ln(t),y(t), singsol=all)
\[ y \left (t \right ) = \left (3 \left (\int t^{1-{\mathrm e}^{-t}} {\mathrm e}^{-t -\operatorname {expIntegral}_{1}\left (t \right )}d t \right )+c_{1} \right ) t^{{\mathrm e}^{-t}} {\mathrm e}^{\operatorname {expIntegral}_{1}\left (t \right )} \]
✓ Solution by Mathematica
Time used: 0.237 (sec). Leaf size: 58
DSolve[3*t==Exp[t]*y'[t]+y[t]*Log[t],y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to t^{e^{-t}} e^{-\operatorname {ExpIntegralEi}(-t)} \left (\int _1^t3 e^{\operatorname {ExpIntegralEi}(-K[1])-K[1]} K[1]^{1-e^{-K[1]}}dK[1]+c_1\right ) \]