Internal problem ID [2092]
Book: Differential equations and linear algebra, Stephen W. Goode and Scott A Annin. Fourth edition,
2015
Section: Chapter 1, First-Order Differential Equations. Section 1.2, Basic Ideas and Terminology. page
21
Problem number: Problem 21.
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}+b^{2}\right ) y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.005 (sec). Leaf size: 25
dsolve(diff(y(x),x$2)-2*a*diff(y(x),x)+(a^2+b^2)*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = c_{1} {\mathrm e}^{a x} \sin \left (b x \right )+c_{2} {\mathrm e}^{a x} \cos \left (b x \right ) \]
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 31
DSolve[y''[x]-2*a*y'[x]+(a^2+b^2)*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to e^{x (a-i b)} \left (c_2 e^{2 i b x}+c_1\right ) \\ \end{align*}