73.8.23 problem 13.4 (d)

Internal problem ID [15152]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 13. Higher order equations: Extending first order concepts. Additional exercises page 259
Problem number : 13.4 (d)
Date solved : Thursday, March 13, 2025 at 05:47:52 AM
CAS classification : [[_2nd_order, _missing_x]]

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

✓ Maple. Time used: 0.003 (sec). Leaf size: 10

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

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

✓ Mathematica. Time used: 0.012 (sec). Leaf size: 14

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

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

✓ Sympy. Time used: 0.063 (sec). Leaf size: 8

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

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