Internal problem ID [11694]
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 (i).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_x]]
\[ \boxed {x^{\prime \prime }-3 x^{\prime }+2 x=0} \] With initial conditions \begin {align*} [x \left (0\right ) = 2, x^{\prime }\left (0\right ) = 6] \end {align*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 15
dsolve([diff(x(t),t$2)-3*diff(x(t),t)+2*x(t)=0,x(0) = 2, D(x)(0) = 6],x(t), singsol=all)
\[ x \left (t \right ) = -2 \,{\mathrm e}^{t}+4 \,{\mathrm e}^{2 t} \]
✓ Solution by Mathematica
Time used: 0.02 (sec). Leaf size: 17
DSolve[{x''[t]-3*x'[t]+2*x[t]==0,{x[0]==2,x'[0]==6}},x[t],t,IncludeSingularSolutions -> True]
\[ x(t)\to 2 e^t \left (2 e^t-1\right ) \]