76.15.12 problem 12

Internal problem ID [17653]
Book : Differential equations. An introduction to modern methods and applications. James Brannan, William E. Boyce. Third edition. Wiley 2015
Section : Chapter 4. Second order linear equations. Section 4.5 (Nonhomogeneous Equations, Method of Undetermined Coefficients). Problems at page 260
Problem number : 12
Date solved : Tuesday, January 28, 2025 at 10:47:35 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }+y&=3 \sin \left (2 t \right )+t \cos \left (2 t \right ) \end{align*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 26

dsolve(diff(y(t),t$2)+y(t)=3*sin(2*t)+t*cos(2*t),y(t), singsol=all)
 

\[ y = c_{2} \sin \left (t \right )+\cos \left (t \right ) c_{1} -\frac {5 \sin \left (2 t \right )}{9}-\frac {\cos \left (2 t \right ) t}{3} \]

✓ Solution by Mathematica

Time used: 0.014 (sec). Leaf size: 33

DSolve[D[y[t],{t,2}]+y[t]==3*Sin[2*t]+t*Cos[2*t],y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to -\frac {5}{9} \sin (2 t)-\frac {1}{3} t \cos (2 t)+c_1 \cos (t)+c_2 \sin (t) \]