65.6.1 problem 12.1 (i)

Internal problem ID [13750]
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)
Date solved : Tuesday, January 28, 2025 at 06:01:48 AM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} x^{\prime \prime }-3 x^{\prime }+2 x&=0 \end{align*}

With initial conditions

\begin{align*} x \left (0\right )&=2\\ x^{\prime }\left (0\right )&=6 \end{align*}

✓ Solution by Maple

Time used: 0.017 (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)
 

\[ x \left (t \right ) = 4 \,{\mathrm e}^{2 t}-2 \,{\mathrm e}^{t} \]

✓ Solution by Mathematica

Time used: 0.013 (sec). Leaf size: 17

DSolve[{D[x[t],{t,2}]-3*D[x[t],t]+2*x[t]==0,{x[0]==2,Derivative[1][x][0 ]==6}},x[t],t,IncludeSingularSolutions -> True]
 

\[ x(t)\to 2 e^t \left (2 e^t-1\right ) \]