65.6.11 problem 12.1 (xi)

Internal problem ID [13760]
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)
Date solved : Tuesday, January 28, 2025 at 06:02:11 AM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} 4 x^{\prime \prime }-20 x^{\prime }+21 x&=0 \end{align*}

With initial conditions

\begin{align*} x \left (0\right )&=-4\\ x^{\prime }\left (0\right )&=-12 \end{align*}

✓ Solution by Maple

Time used: 0.018 (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: 0.015 (sec). Leaf size: 23

DSolve[{4*D[x[t],{t,2}]-20*D[x[t],t]+21*x[t]==0,{x[0]==-4,Derivative[1][x][0 ]==-12}},x[t],t,IncludeSingularSolutions -> True]
 

\[ x(t)\to -e^{3 t/2} \left (3 e^{2 t}+1\right ) \]