15.18.10 problem 10

Internal problem ID [3253]
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 : 10
Date solved : Monday, January 27, 2025 at 07:28:50 AM
CAS classification : [[_2nd_order, _missing_y]]

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

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 23

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

\[ y \left (x \right ) = -\frac {\ln \left (x \right ) x^{2}}{2}+\frac {\left (2 c_{1} +1\right ) x^{2}}{4}+c_2 \]

✓ Solution by Mathematica

Time used: 0.034 (sec). Leaf size: 30

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

\[ y(x)\to -\frac {1}{2} x^2 \log (x)+\frac {1}{4} (1+2 c_1) x^2+c_2 \]