20.1.13 problem Problem 19

Internal problem ID [3570]
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
Date solved : Monday, January 27, 2025 at 07:44:33 AM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }-\left (a +b \right ) y^{\prime }+a b y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.003 (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)
 

\[ y \left (x \right ) = c_{1} {\mathrm e}^{b x}+c_{2} {\mathrm e}^{a x} \]

✓ Solution by Mathematica

Time used: 0.015 (sec). Leaf size: 22

DSolve[D[y[x],{x,2}]-(a+b)*D[y[x],x]+a*b*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to c_2 e^{a x}+c_1 e^{b x} \]