77.32.1 problem 1

Internal problem ID [20685]
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 : Thursday, October 02, 2025 at 06:18:39 PM
CAS classification : [[_2nd_order, _missing_x]]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 14

ode:=a*diff(diff(y(x),x),x) = diff(y(x),x); 
dsolve(ode,y(x), singsol=all);
 

\[ y = c_1 +c_2 \,{\mathrm e}^{\frac {x}{a}} \]

✓ Mathematica. Time used: 0.01 (sec). Leaf size: 19

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

\begin{align*} y(x)&\to a c_1 e^{\frac {x}{a}}+c_2 \end{align*}

✓ Sympy. Time used: 0.074 (sec). Leaf size: 10

from sympy import * 
x = symbols("x") 
a = symbols("a") 
y = Function("y") 
ode = Eq(a*Derivative(y(x), (x, 2)) - Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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