14.11.9 problem 9

Internal problem ID [2602]
Book : Differential equations and their applications, 4th ed., M. Braun
Section : Chapter 2. Second order differential equations. Section 2.5. Method of judicious guessing. Excercises page 164
Problem number : 9
Date solved : Monday, January 27, 2025 at 06:02:25 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }-2 y^{\prime }+5 y&=2 \cos \left (t \right )^{2} \end{align*}

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 33

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

\[ y = \frac {\left (85 c_2 \,{\mathrm e}^{t}-20\right ) \sin \left (2 t \right )}{85}+{\mathrm e}^{t} \cos \left (2 t \right ) c_1 +\frac {\cos \left (2 t \right )}{17}+\frac {1}{5} \]

✓ Solution by Mathematica

Time used: 0.388 (sec). Leaf size: 39

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

\[ y(t)\to \left (\frac {1}{17}+c_2 e^t\right ) \cos (2 t)+\left (-\frac {4}{17}+c_1 e^t\right ) \sin (2 t)+\frac {1}{5} \]