83.32.1 problem 1

Internal problem ID [19400]
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 (F) at page 113
Problem number : 1
Date solved : Tuesday, January 28, 2025 at 01:37:53 PM
CAS classification : [[_2nd_order, _missing_x]]

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 14

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

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

✓ Solution by Mathematica

Time used: 0.011 (sec). Leaf size: 19

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

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