Internal problem ID [2090]
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 19.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_x]]
Solve \begin {gather*} \boxed {y^{\prime \prime }-\left (a +b \right ) y^{\prime }+a b y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.004 (sec). Leaf size: 17
dsolve(diff(y(x),x$2)-(a+b)*diff(y(x),x)+a*b*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = c_{1} {\mathrm e}^{b x}+c_{2} {\mathrm e}^{a x} \]
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 22
DSolve[y''[x]-(a+b)*y'[x]+a*b*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to c_2 e^{a x}+c_1 e^{b x} \\ \end{align*}