Internal problem ID [639]
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: 23.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_x]]
Solve \begin {gather*} \boxed {u^{\prime \prime }-u^{\prime }+2 u=0} \end {gather*} With initial conditions \begin {align*} [u \relax (0) = 2, u^{\prime }\relax (0) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.034 (sec). Leaf size: 31
dsolve([diff(u(x),x$2)- diff(u(x),x)+2*u(x) = 0,u(0) = 2, D(u)(0) = 0],u(x), singsol=all)
\[ u \relax (x ) = -\frac {2 \,{\mathrm e}^{\frac {x}{2}} \left (\sqrt {7}\, \sin \left (\frac {\sqrt {7}\, x}{2}\right )-7 \cos \left (\frac {\sqrt {7}\, x}{2}\right )\right )}{7} \]
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 19
DSolve[{u''[x]+4*u'[x]+5*u[x]==0,{u[0]==2,u'[0]==0}},u[x],x,IncludeSingularSolutions -> True]
\begin{align*} u(x)\to 2 e^{-2 x} (2 \sin (x)+\cos (x)) \\ \end{align*}