76.15.4 problem 4

Internal problem ID [17645]
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 : 4
Date solved : Tuesday, January 28, 2025 at 10:47:17 AM
CAS classification : [[_2nd_order, _missing_y]]

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

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 28

dsolve(diff(y(t),t$2)+2*diff(y(t),t)=3+4*sin(2*t),y(t), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.284 (sec). Leaf size: 38

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

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