10.8.18 problem 24

Internal problem ID [1290]
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
Date solved : Monday, January 27, 2025 at 04:50:01 AM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} 5 u^{\prime \prime }+2 u^{\prime }+7 u&=0 \end{align*}

With initial conditions

\begin{align*} u \left (0\right )&=2\\ u^{\prime }\left (0\right )&=1 \end{align*}

✓ Solution by Maple

Time used: 0.033 (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)
 

\[ u = \frac {{\mathrm e}^{-\frac {x}{5}} \left (7 \sqrt {34}\, \sin \left (\frac {\sqrt {34}\, x}{5}\right )+68 \cos \left (\frac {\sqrt {34}\, x}{5}\right )\right )}{34} \]

✓ Solution by Mathematica

Time used: 0.025 (sec). Leaf size: 48

DSolve[{5*D[u[x],{x,2}]+2*D[u[x],x]+7*u[x]==0,{u[0]==2,Derivative[1][u][0]==1}},u[x],x,IncludeSingularSolutions -> True]
 

\[ u(x)\to \frac {1}{34} e^{-x/5} \left (7 \sqrt {34} \sin \left (\frac {\sqrt {34} x}{5}\right )+68 \cos \left (\frac {\sqrt {34} x}{5}\right )\right ) \]