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]]
\[ \boxed {y^{\prime \prime }+2 a y^{\prime }+\left (a^{2}+1\right ) y=0} \] With initial conditions \begin {align*} [y \left (0\right ) = 1, y^{\prime }\left (0\right ) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.015 (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)
\[ y \left (x \right ) = {\mathrm e}^{-a x} \left (a \sin \left (x \right )+\cos \left (x \right )\right ) \]
✓ Solution by Mathematica
Time used: 0.031 (sec). Leaf size: 94
DSolve[{y''[x]+2*a*y'[x]+(a^1+1)*y[x]==0,{y[0]==1,y'[0]==0}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {e^{-\left (\left (\sqrt {a^2-a-1}+a\right ) x\right )} \left (a \left (e^{2 \sqrt {a^2-a-1} x}-1\right )+\sqrt {a^2-a-1} \left (e^{2 \sqrt {a^2-a-1} x}+1\right )\right )}{2 \sqrt {a^2-a-1}} \]