76.15.20 problem 21

Internal problem ID [17661]
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 : 21
Date solved : Tuesday, January 28, 2025 at 10:48:23 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }+4 y&=3 \sin \left (2 t \right ) \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=2\\ y^{\prime }\left (0\right )&=-1 \end{align*}

✓ Solution by Maple

Time used: 0.018 (sec). Leaf size: 24

dsolve([diff(y(t),t$2)+4*y(t)=3*sin(2*t),y(0) = 2, D(y)(0) = -1],y(t), singsol=all)
 

\[ y = -\frac {\sin \left (2 t \right )}{8}+2 \cos \left (2 t \right )-\frac {3 \cos \left (2 t \right ) t}{4} \]

✓ Solution by Mathematica

Time used: 0.077 (sec). Leaf size: 26

DSolve[{D[y[t],{t,2}]+4*y[t]==3*Sin[2*t],{y[0]==2,Derivative[1][y][0] ==-1}},y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to \left (2-\frac {3 t}{4}\right ) \cos (2 t)-\frac {1}{8} \sin (2 t) \]