Internal problem ID [11704]
Book: AN INTRODUCTION TO ORDINARY DIFFERENTIAL EQUATIONS by JAMES C.
ROBINSON. Cambridge University Press 2004
Section: Chapter 12, Homogeneous second order linear equations. Exercises page 118
Problem number: 12.1 (xi).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_x]]
\[ \boxed {4 x^{\prime \prime }-20 x^{\prime }+21 x=0} \] With initial conditions \begin {align*} [x \left (0\right ) = -4, x^{\prime }\left (0\right ) = -12] \end {align*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 17
dsolve([4*diff(x(t),t$2)-20*diff(x(t),t)+21*x(t)=0,x(0) = -4, D(x)(0) = -12],x(t), singsol=all)
\[ x \left (t \right ) = -3 \,{\mathrm e}^{\frac {7 t}{2}}-{\mathrm e}^{\frac {3 t}{2}} \]
✓ Solution by Mathematica
Time used: 0.023 (sec). Leaf size: 23
DSolve[{4*x''[t]-20*x'[t]+21*x[t]==0,{x[0]==-4,x'[0]==-12}},x[t],t,IncludeSingularSolutions -> True]
\[ x(t)\to -e^{3 t/2} \left (3 e^{2 t}+1\right ) \]