15.18.12 problem 12

Internal problem ID [3255]
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 : 12
Date solved : Monday, January 27, 2025 at 07:28:53 AM
CAS classification : [[_2nd_order, _missing_y]]

\begin{align*} x^{2} y^{\prime \prime }&=x y^{\prime }+1 \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 16

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

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

✓ Solution by Mathematica

Time used: 0.016 (sec). Leaf size: 23

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

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