8.9 problem 12

Internal problem ID [1095]

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.
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 }+y a^{2}=0} \end {gather*}

Solution by Maple

Time used: 0.016 (sec). Leaf size: 18

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

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

Solution by Mathematica

Time used: 0.003 (sec). Leaf size: 18

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

\begin{align*} y(x)\to e^{a x} (c_2 x+c_1) \\ \end{align*}