10.8.16 problem 22

Internal problem ID [1288]
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 : 22
Date solved : Monday, January 27, 2025 at 04:49:55 AM
CAS classification : [[_2nd_order, _missing_x]]

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

With initial conditions

\begin{align*} y \left (\frac {\pi }{4}\right )&=2\\ y^{\prime }\left (\frac {\pi }{4}\right )&=-2 \end{align*}

✓ Solution by Maple

Time used: 0.039 (sec). Leaf size: 21

dsolve([diff(y(x),x$2)+ 2*diff(y(x),x)+2*y(x) = 0,y(1/4*Pi) = 2, D(y)(1/4*Pi) = -2],y(x), singsol=all)
 

\[ y = \sqrt {2}\, {\mathrm e}^{-x +\frac {\pi }{4}} \left (\sin \left (x \right )+\cos \left (x \right )\right ) \]

✓ Solution by Mathematica

Time used: 0.017 (sec). Leaf size: 27

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

\[ y(x)\to \sqrt {2} e^{\frac {\pi }{4}-x} (\sin (x)+\cos (x)) \]