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 : Monday, January 27, 2025 at 07:28:44 AM
CAS classification : [[_2nd_order, _missing_y]]

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 12

dsolve((1-x)*diff(y(x),x$2)=diff(y(x),x),y(x), singsol=all)
 

\[ y \left (x \right ) = c_2 \ln \left (x -1\right )+c_{1} \]

✓ Solution by Mathematica

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

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

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