83.29.1 problem 1

Internal problem ID [19374]
Book : A Text book for differentional equations for postgraduate students by Ray and Chaturvedi. First edition, 1958. BHASKAR press. INDIA
Section : Chapter VII. Exact differential equations and certain particular forms of equations. Exercise VII (C) at page 107
Problem number : 1
Date solved : Tuesday, January 28, 2025 at 01:35:44 PM
CAS classification : [[_2nd_order, _missing_x]]

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

✓ Solution by Maple

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

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

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

✓ Solution by Mathematica

Time used: 0.011 (sec). Leaf size: 20

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

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