Internal problem ID [642]
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: 26.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_x]]
Solve \begin {gather*} \boxed {y^{\prime \prime }+2 a y^{\prime }+\left (a^{2}+1\right ) y=0} \end {gather*} With initial conditions \begin {align*} [y \relax (0) = 1, y^{\prime }\relax (0) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 17
dsolve([diff(y(x),x$2)+ 2*a*diff(y(x),x)+(a^2+1)*y(x) = 0,y(0) = 1, D(y)(0) = 0],y(x), singsol=all)
\[ y \relax (x ) = {\mathrm e}^{-a x} \left (a \sin \relax (x )+\cos \relax (x )\right ) \]
✓ Solution by Mathematica
Time used: 0.011 (sec). Leaf size: 54
DSolve[{y''[x]+2*a*y'[x]+(a^1+1)*y[x]==0,{y[0]==1,y'[0]==0}},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to e^{-a x} \left (\frac {a \sinh \left (\sqrt {(a-1) a-1} x\right )}{\sqrt {(a-1) a-1}}+\cosh \left (\sqrt {(a-1) a-1} x\right )\right ) \\ \end{align*}