39.1.4 problem Problem 11.4

Internal problem ID [6509]
Book : Schaums Outline Differential Equations, 4th edition. Bronson and Costa. McGraw Hill 2014
Section : Chapter 11. THE METHOD OF UNDETERMINED COEFFICIENTS. page 95
Problem number : Problem 11.4
Date solved : Monday, January 27, 2025 at 02:09:35 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }-6 y^{\prime }+25 y&=2 \sin \left (\frac {t}{2}\right )-\cos \left (\frac {t}{2}\right ) \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 37

dsolve(diff(y(t),t$2)-6*diff(y(t),t)+25*y(t)=2*sin(t/2)-cos(t/2),y(t), singsol=all)
 

\[ y = {\mathrm e}^{3 t} \sin \left (4 t \right ) c_2 +{\mathrm e}^{3 t} \cos \left (4 t \right ) c_1 +\frac {56 \sin \left (\frac {t}{2}\right )}{663}-\frac {20 \cos \left (\frac {t}{2}\right )}{663} \]

✓ Solution by Mathematica

Time used: 0.025 (sec). Leaf size: 51

DSolve[D[y[t],{t,2}]-6*D[y[t],t]+25*y[t]==2*Sin[t/2]-Cos[t/2],y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to \frac {1}{663} \left (56 \sin \left (\frac {t}{2}\right )-20 \cos \left (\frac {t}{2}\right )\right )+c_2 e^{3 t} \cos (4 t)+c_1 e^{3 t} \sin (4 t) \]