63.9.15 problem 2(c)

Internal problem ID [13142]
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 2.3.1 Nonhomogeneous Equations: Undetermined Coefficients. Exercises page 110
Problem number : 2(c)
Date solved : Tuesday, January 28, 2025 at 05:06:25 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} x^{\prime \prime }+x&=t^{2} \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 17

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

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

✓ Solution by Mathematica

Time used: 0.012 (sec). Leaf size: 20

DSolve[D[x[t],{t,2}]+x[t]==t^2,x[t],t,IncludeSingularSolutions -> True]
 

\[ x(t)\to t^2+c_1 \cos (t)+c_2 \sin (t)-2 \]