35.9.10 problem 5, using elementary method

Internal problem ID [6245]
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 : 5, using elementary method
Date solved : Monday, January 27, 2025 at 01:49:57 PM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }&=y \end{align*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 15

dsolve(diff(y(x),x$2)=y(x),y(x), singsol=all)
 

\[ y = {\mathrm e}^{-x} c_{1} +c_{2} {\mathrm e}^{x} \]

✓ Solution by Mathematica

Time used: 0.012 (sec). Leaf size: 20

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

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