14.11.7 problem 7

Internal problem ID [2600]
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 : 7
Date solved : Monday, January 27, 2025 at 06:02:18 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }+4 y&=t \sin \left (2 t \right ) \end{align*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 31

dsolve(diff(y(t),t$2)+4*y(t)=t*sin(2*t),y(t), singsol=all)
 

\[ y = \frac {\left (-t^{2}+8 c_1 \right ) \cos \left (2 t \right )}{8}+\frac {\sin \left (2 t \right ) \left (t +16 c_2 \right )}{16} \]

✓ Solution by Mathematica

Time used: 0.098 (sec). Leaf size: 38

DSolve[D[y[t],{t,2}]+4*y[t]==t*Sin[2*t],y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to \frac {1}{64} \left (\left (-8 t^2+1+64 c_1\right ) \cos (2 t)+4 (t+16 c_2) \sin (2 t)\right ) \]