67.5.7 problem Problem 2(b)

Internal problem ID [14093]
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)
Date solved : Tuesday, January 28, 2025 at 06:14:14 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }-2 y^{\prime }+5 y&={\mathrm e}^{t} \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 21

dsolve(diff(y(t),t$2)-2*diff(y(t),t)+5*y(t)=exp(t),y(t), singsol=all)
 

\[ y = {\mathrm e}^{t} \left (\frac {1}{4}+\sin \left (2 t \right ) c_{2} +\cos \left (2 t \right ) c_{1} \right ) \]

✓ Solution by Mathematica

Time used: 0.034 (sec). Leaf size: 57

DSolve[D[y[t],{t,2}]-2*D[y[t],t]+5*y[t]==Exp[t],y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to \frac {1}{2} e^t \left (2 \sin (2 t) \int _1^t\frac {1}{2} \cos (2 K[1])dK[1]+\cos (2 t) \left (\cos ^2(t)+2 c_2\right )+2 c_1 \sin (2 t)\right ) \]