Internal problem ID [11738]
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).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_y]]
\[ \boxed {x^{\prime \prime }-4 x^{\prime }=\tan \left (t \right )} \]
✓ Solution by Maple
Time used: 0.0 (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: 60.232 (sec). Leaf size: 82
DSolve[x''[t]-4*x'[t]==Tan[t],x[t],t,IncludeSingularSolutions -> True]
\[ x(t)\to \int _1^t\left (e^{4 K[1]} c_1+\frac {1}{20} \left (-5 i \operatorname {Hypergeometric2F1}\left (2 i,1,1+2 i,-e^{2 i K[1]}\right )-(2-4 i) e^{2 i K[1]} \operatorname {Hypergeometric2F1}\left (1,1+2 i,2+2 i,-e^{2 i K[1]}\right )\right )\right )dK[1]+c_2 \]