Internal problem ID [638]
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.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_x]]
Solve \begin {gather*} \boxed {y^{\prime \prime }+2 y^{\prime }+2 y=0} \end {gather*} With initial conditions \begin {align*} \left [y \left (\frac {\pi }{4}\right ) = 2, y^{\prime }\left (\frac {\pi }{4}\right ) = -2\right ] \end {align*}
✓ Solution by Maple
Time used: 0.031 (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)
\[ y \relax (x ) = {\mathrm e}^{-x +\frac {\pi }{4}} \sqrt {2}\, \left (\sin \relax (x )+\cos \relax (x )\right ) \]
✓ Solution by Mathematica
Time used: 0.004 (sec). Leaf size: 27
DSolve[{y''[x]+2*y'[x]+2*y[x]==0,{y[Pi/4]==2,y'[Pi/4]==-2}},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \sqrt {2} e^{\frac {\pi }{4}-x} (\sin (x)+\cos (x)) \\ \end{align*}