67.8.2 problem 13.1 (b)

Internal problem ID [16497]
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 : 13.1 (b)
Date solved : Thursday, October 02, 2025 at 01:35:35 PM
CAS classification : [[_2nd_order, _missing_y]]

\begin{align*} x y^{\prime \prime }&=2 y^{\prime } \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 11

ode:=x*diff(diff(y(x),x),x) = 2*diff(y(x),x); 
dsolve(ode,y(x), singsol=all);
 

\[ y = c_2 \,x^{3}+c_1 \]

✓ Mathematica. Time used: 0.007 (sec). Leaf size: 19

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

\begin{align*} y(x)&\to \frac {1}{2} c_1 e^{2 x}+c_2 \end{align*}

✓ Sympy. Time used: 0.071 (sec). Leaf size: 8

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

\[ y{\left (x \right )} = C_{1} + C_{2} x^{3} \]