33.1.4 problem Problem 11.4

Internal problem ID [7796]
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 : Tuesday, September 30, 2025 at 05:05:34 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*}

✓ Maple. Time used: 0.004 (sec). Leaf size: 37

ode:=diff(diff(y(t),t),t)-6*diff(y(t),t)+25*y(t) = 2*sin(1/2*t)-cos(1/2*t); 
dsolve(ode,y(t), singsol=all);
 

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

✓ Mathematica. Time used: 0.015 (sec). Leaf size: 51

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

\begin{align*} 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) \end{align*}

✓ Sympy. Time used: 0.157 (sec). Leaf size: 37

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(25*y(t) - 2*sin(t/2) + cos(t/2) - 6*Derivative(y(t), t) + Derivative(y(t), (t, 2)),0) 
ics = {} 
dsolve(ode,func=y(t),ics=ics)
 

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