76.15.23 problem 24

Internal problem ID [17664]
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 : 24
Date solved : Tuesday, January 28, 2025 at 10:49:55 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }+y&=t \left (1+\sin \left (t \right )\right ) \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 28

dsolve(diff(y(t),t$2)+y(t)=t*(1+sin(t)),y(t), singsol=all)
 

\[ y = \frac {\left (-t^{2}+4 c_{1} \right ) \cos \left (t \right )}{4}+\frac {\left (4 c_{2} +t \right ) \sin \left (t \right )}{4}+t \]

✓ Solution by Mathematica

Time used: 0.083 (sec). Leaf size: 34

DSolve[D[y[t],{t,2}]+y[t]==t*(1+Sin[t]),y[t],t,IncludeSingularSolutions -> True]
 

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