75.15.1 problem 432

Internal problem ID [16952]
Book : A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV, G.I. MARKARENKO. MIR, MOSCOW. 1983
Section : Chapter 2 (Higher order ODEs). Section 15.2 Homogeneous differential equations with constant coefficients. Exercises page 121
Problem number : 432
Date solved : Tuesday, January 28, 2025 at 09:43:36 AM
CAS classification : [[_2nd_order, _missing_x]]

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 15

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

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

✓ Solution by Mathematica

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

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

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