Internal problem ID [635]
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.
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 }+5 y=0} \end {gather*} With initial conditions \begin {align*} \left [y \left (\frac {\pi }{2}\right ) = 0, y^{\prime }\left (\frac {\pi }{2}\right ) = 2\right ] \end {align*}
✓ Solution by Maple
Time used: 0.016 (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)
\[ y \relax (x ) = -\sin \left (2 x \right ) {\mathrm e}^{-\frac {\pi }{2}+x} \]
✓ Solution by Mathematica
Time used: 0.004 (sec). Leaf size: 20
DSolve[{y''[x]-2*y'[x]+5*y[x]==0,{y[Pi/2]==0,y'[Pi/2]==2}},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -e^{x-\frac {\pi }{2}} \sin (2 x) \\ \end{align*}