Internal problem ID [14595]
Book: INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton.
Fourth edition 2014. ElScAe. 2014
Section: Chapter 4. Higher Order Equations. Exercises 4.4, page 163
Problem number: 20.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }-2 y^{\prime }+y=\frac {{\mathrm e}^{t}}{t}} \]
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 18
dsolve(diff(y(t),t$2)-2*diff(y(t),t)+y(t)=1/t*exp(t),y(t), singsol=all)
\[ y \left (t \right ) = \left (t \ln \left (t \right )+t \left (c_{1} -1\right )+c_{2} \right ) {\mathrm e}^{t} \]
✓ Solution by Mathematica
Time used: 0.02 (sec). Leaf size: 22
DSolve[y''[t]-2*y'[t]+y[t]==1/t*Exp[t],y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to e^t (t \log (t)+(-1+c_2) t+c_1) \]