Internal problem ID [11009]
Book: APPLIED DIFFERENTIAL EQUATIONS The Primary Course by Vladimir A. Dobrushkin.
CRC Press 2015
Section: Chapter 6. Introduction to Systems of ODEs. Problems page 408
Problem number: Problem 2(b).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {y^{\prime \prime }-2 y^{\prime }+5 y-{\mathrm e}^{t}=0} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 25
dsolve(diff(y(t),t$2)-2*diff(y(t),t)+5*y(t)=exp(t),y(t), singsol=all)
\[ y \left (t \right ) = {\mathrm e}^{t} \sin \left (2 t \right ) c_{2} +{\mathrm e}^{t} \cos \left (2 t \right ) c_{1} +\frac {{\mathrm e}^{t}}{4} \]
✓ Solution by Mathematica
Time used: 0.011 (sec). Leaf size: 33
DSolve[y''[t]-2*y'[t]+5*y[t]==Exp[t],y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to \frac {1}{4} e^t ((1+4 c_2) \cos (2 t)+4 c_1 \sin (2 t)+1) \\ \end{align*}