10.8.17 problem 23

Internal problem ID [1289]
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
Date solved : Monday, January 27, 2025 at 04:49:57 AM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} u^{\prime \prime }-u^{\prime }+2 u&=0 \end{align*}

With initial conditions

\begin{align*} u \left (0\right )&=2\\ u^{\prime }\left (0\right )&=0 \end{align*}

✓ Solution by Maple

Time used: 0.408 (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)
 

\[ u = -\frac {2 \,{\mathrm e}^{\frac {x}{2}} \left (\sqrt {7}\, \sin \left (\frac {\sqrt {7}\, x}{2}\right )-7 \cos \left (\frac {\sqrt {7}\, x}{2}\right )\right )}{7} \]

✓ Solution by Mathematica

Time used: 0.015 (sec). Leaf size: 19

DSolve[{D[u[x],{x,2}]+4*D[u[x],x]+5*u[x]==0,{u[0]==2,Derivative[1][u][0]==0}},u[x],x,IncludeSingularSolutions -> True]
 

\[ u(x)\to 2 e^{-2 x} (2 \sin (x)+\cos (x)) \]