65.11.5 problem 18.1 (v)

Internal problem ID [13794]
Book : AN INTRODUCTION TO ORDINARY DIFFERENTIAL EQUATIONS by JAMES C. ROBINSON. Cambridge University Press 2004
Section : Chapter 18, The variation of constants formula. Exercises page 168
Problem number : 18.1 (v)
Date solved : Tuesday, January 28, 2025 at 06:03:40 AM
CAS classification : [[_2nd_order, _missing_y]]

\begin{align*} x^{\prime \prime }-4 x^{\prime }&=\tan \left (t \right ) \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 24

dsolve(diff(x(t),t$2)-4*diff(x(t),t)=tan(t),x(t), singsol=all)
 

\[ x \left (t \right ) = \int \left (\int \tan \left (t \right ) {\mathrm e}^{-4 t}d t +c_{1} \right ) {\mathrm e}^{4 t}d t +c_{2} \]

✓ Solution by Mathematica

Time used: 5.055 (sec). Leaf size: 43

DSolve[D[x[t],{t,2}]-4*D[x[t],t]==Tan[t],x[t],t,IncludeSingularSolutions -> True]
 

\[ x(t)\to \int _1^te^{4 K[2]} \left (c_1+\int _1^{K[2]}e^{-4 K[1]} \tan (K[1])dK[1]\right )dK[2]+c_2 \]