82.48.18 problem Ex. 18

Internal problem ID [18928]
Book : Introductory Course On Differential Equations by Daniel A Murray. Longmans Green and Co. NY. 1924
Section : Chapter VIII. End of chapter problems at page 107
Problem number : Ex. 18
Date solved : Monday, March 31, 2025 at 06:25:14 PM
CAS classification : [[_2nd_order, _missing_x]]

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

✓ Maple. Time used: 0.004 (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: 0.017 (sec). Leaf size: 19

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

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

✓ Sympy. Time used: 0.124 (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)
 

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