12.8.9 problem 12

Internal problem ID [1745]
Book : Elementary differential equations with boundary value problems. William F. Trench. Brooks/Cole 2001
Section : Chapter 5 linear second order equations. Section 5.1 Homogeneous linear equations. Page 203
Problem number : 12
Date solved : Monday, January 27, 2025 at 05:34:09 AM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }-2 a y^{\prime }+a^{2} y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 14

dsolve(diff(y(x),x$2)-2*a*diff(y(x),x)+a^2*y(x)=0,y(x), singsol=all)
 

\[ y = {\mathrm e}^{a x} \left (c_2 x +c_1 \right ) \]

✓ Solution by Mathematica

Time used: 0.015 (sec). Leaf size: 18

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

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