Internal problem ID [2284]
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.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_y]]
\[ \boxed {x^{2} y^{\prime \prime }-y^{\prime } x=1} \]
✓ Solution by Maple
Time used: 0.0 (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: 0.012 (sec). Leaf size: 23
DSolve[x^2*y''[x]==x*y'[x]+1,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {c_1 x^2}{2}-\frac {\log (x)}{2}+c_2 \]