Internal problem ID [640]
Book: Elementary differential equations and boundary value problems, 10th ed., Boyce and
DiPrima
Section: Chapter 3, Second order linear equations, 3.3 Complex Roots of the Characteristic Equation ,
page 164
Problem number: 24.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_x]]
Solve \begin {gather*} \boxed {5 u^{\prime \prime }+2 u^{\prime }+7 u=0} \end {gather*} With initial conditions \begin {align*} [u \relax (0) = 2, u^{\prime }\relax (0) = 1] \end {align*}
✓ Solution by Maple
Time used: 0.04 (sec). Leaf size: 32
dsolve([5*diff(u(x),x$2)+ 2*diff(u(x),x)+7*u(x) = 0,u(0) = 2, D(u)(0) = 1],u(x), singsol=all)
\[ u \relax (x ) = \frac {{\mathrm e}^{-\frac {x}{5}} \left (7 \sqrt {34}\, \sin \left (\frac {\sqrt {34}\, x}{5}\right )+68 \cos \left (\frac {\sqrt {34}\, x}{5}\right )\right )}{34} \]
✓ Solution by Mathematica
Time used: 0.005 (sec). Leaf size: 48
DSolve[{5*u''[x]+2*u'[x]+7*u[x]==0,{u[0]==2,u'[0]==1}},u[x],x,IncludeSingularSolutions -> True]
\begin{align*} u(x)\to \frac {1}{34} e^{-x/5} \left (7 \sqrt {34} \sin \left (\frac {\sqrt {34} x}{5}\right )+68 \cos \left (\frac {\sqrt {34} x}{5}\right )\right ) \\ \end{align*}