63.12.5 problem 1(e)

Internal problem ID [13167]
Book : A First Course in Differential Equations by J. David Logan. Third Edition. Springer-Verlag, NY. 2015.
Section : Chapter 2, Second order linear equations. Section 2.4.2 Variation of parameters. Exercises page 124
Problem number : 1(e)
Date solved : Tuesday, January 28, 2025 at 05:11:44 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} x^{\prime \prime }+x&=\frac {1}{1+t} \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 32

dsolve(diff(x(t),t$2)+x(t)=1/(1+t),x(t), singsol=all)
 

\[ x \left (t \right ) = c_{2} \sin \left (t \right )+\cos \left (t \right ) c_{1} -\operatorname {Si}\left (t +1\right ) \cos \left (t +1\right )+\operatorname {Ci}\left (t +1\right ) \sin \left (t +1\right ) \]

✓ Solution by Mathematica

Time used: 0.082 (sec). Leaf size: 57

DSolve[D[x[t],{t,2}]+x[t]==1/(1+t),x[t],t,IncludeSingularSolutions -> True]
 

\[ x(t)\to \cos (t) \int _1^t-\frac {\sin (K[1])}{K[1]+1}dK[1]+\sin (t) \int _1^t\frac {\cos (K[2])}{K[2]+1}dK[2]+c_1 \cos (t)+c_2 \sin (t) \]