35.9.12 problem 6, using elementary method

Internal problem ID [6247]
Book : Mathematical Methods in the Physical Sciences. third edition. Mary L. Boas. John Wiley. 2006
Section : Chapter 12, Series Solutions of Differential Equations. Section 1. Miscellaneous problems. page 564
Problem number : 6, using elementary method
Date solved : Monday, January 27, 2025 at 01:50:01 PM
CAS classification : [[_2nd_order, _missing_x]]

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

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 12

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

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

✓ Solution by Mathematica

Time used: 0.012 (sec). Leaf size: 16

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

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