Internal problem ID [4539]
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).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_x]]
Solve \begin {gather*} \boxed {x^{\prime \prime }+42 x^{\prime }+x=0} \end {gather*} With initial conditions \begin {align*} [x \relax (0) = 1, x^{\prime }\relax (0) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.048 (sec). Leaf size: 42
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)
\[ x \relax (t ) = \frac {{\mathrm e}^{\left (-21+2 \sqrt {110}\right ) t}}{2}+\frac {21 \,{\mathrm e}^{\left (-21+2 \sqrt {110}\right ) t} \sqrt {110}}{440}+\frac {{\mathrm e}^{-2 t \sqrt {110}-21 t}}{2}-\frac {21 \,{\mathrm e}^{-2 t \sqrt {110}-21 t} \sqrt {110}}{440} \]
✓ Solution by Mathematica
Time used: 0.007 (sec). Leaf size: 53
DSolve[{x''[t]+42*x'[t]+x[t]==0,{x[0]==1,x'[0]==0}},x[t],t,IncludeSingularSolutions -> True]
\begin{align*} 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}} \\ \end{align*}