10.8.13 problem 19

Internal problem ID [1285]
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 : 19
Date solved : Monday, January 27, 2025 at 04:49:46 AM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }-2 y^{\prime }+5 y&=0 \end{align*}

With initial conditions

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

✓ Solution by Maple

Time used: 0.034 (sec). Leaf size: 16

dsolve([diff(y(x),x$2)- 2*diff(y(x),x)+5*y(x) = 0,y(1/2*Pi) = 0, D(y)(1/2*Pi) = 2],y(x), singsol=all)
 

\[ y = -\sin \left (2 x \right ) {\mathrm e}^{-\frac {\pi }{2}+x} \]

✓ Solution by Mathematica

Time used: 0.015 (sec). Leaf size: 20

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

\[ y(x)\to -e^{x-\frac {\pi }{2}} \sin (2 x) \]