15.18.7 problem 7

Internal problem ID [3250]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 35, page 157
Problem number : 7
Date solved : Sunday, March 30, 2025 at 01:25:04 AM
CAS classification : [[_2nd_order, _missing_y]]

\begin{align*} \left (1-x \right ) y^{\prime \prime }&=y^{\prime } \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 12

ode:=(1-x)*diff(diff(y(x),x),x) = diff(y(x),x); 
dsolve(ode,y(x), singsol=all);
 

\[ y = c_2 \ln \left (-1+x \right )+c_1 \]

✓ Mathematica. Time used: 0.013 (sec). Leaf size: 18

ode=(1-x)*D[y[x],{x,2}]==D[y[x],x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to c_2-c_1 \log (1-x) \]

✓ Sympy. Time used: 0.172 (sec). Leaf size: 10

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq((1 - x)*Derivative(y(x), (x, 2)) - Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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