14.11.10 problem 10

Internal problem ID [2603]
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 : 10
Date solved : Monday, January 27, 2025 at 06:02:41 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

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

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 30

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

\[ y = \frac {{\mathrm e}^{t} \left (\left (4 c_1 +1\right ) \cos \left (2 t \right )+1+\left (t +4 c_2 \right ) \sin \left (2 t \right )\right )}{4} \]

✓ Solution by Mathematica

Time used: 0.045 (sec). Leaf size: 36

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

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