37.1.3 problem 10.2.8 part(1)

Internal problem ID [6390]
Book : Basic Training in Mathematics. By R. Shankar. Plenum Press. NY. 1995
Section : Chapter 10, Differential equations. Section 10.2, ODEs with constant Coefficients. page 307
Problem number : 10.2.8 part(1)
Date solved : Monday, January 27, 2025 at 01:58:44 PM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} x^{\prime \prime }+42 x^{\prime }+x&=0 \end{align*}

With initial conditions

\begin{align*} x \left (0\right )&=1\\ x^{\prime }\left (0\right )&=0 \end{align*}

✓ Solution by Maple

Time used: 0.045 (sec). Leaf size: 43

dsolve([diff(x(t),t$2)+42*diff(x(t),t)+x(t)=0,x(0) = 1, D(x)(0) = 0],x(t), singsol=all)
 

\[ x \left (t \right ) = \frac {\left (220+21 \sqrt {110}\right ) {\mathrm e}^{\left (-21+2 \sqrt {110}\right ) t}}{440}+\frac {\left (220-21 \sqrt {110}\right ) {\mathrm e}^{\left (-21-2 \sqrt {110}\right ) t}}{440} \]

✓ Solution by Mathematica

Time used: 0.032 (sec). Leaf size: 53

DSolve[{D[x[t],{t,2}]+42*D[x[t],t]+x[t]==0,{x[0]==1,Derivative[1][x][0 ]==0}},x[t],t,IncludeSingularSolutions -> True]
 

\[ x(t)\to \frac {e^{-\left (\left (21+2 \sqrt {110}\right ) t\right )} \left (\left (881+84 \sqrt {110}\right ) e^{4 \sqrt {110} t}-1\right )}{880+84 \sqrt {110}} \]