Internal problem ID [2282]
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.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_y]]
\[ \boxed {x y^{\prime \prime }-y^{\prime }=-x} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 24
dsolve(x*diff(y(x),x$2)+x=diff(y(x),x),y(x), singsol=all)
\[ y \left (x \right ) = -\frac {x^{2} \ln \left (x \right )}{2}+\frac {x^{2}}{4}+\frac {c_{1} x^{2}}{2}+c_{2} \]
✓ Solution by Mathematica
Time used: 0.027 (sec). Leaf size: 30
DSolve[x*y''[x]+x==y'[x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to -\frac {1}{2} x^2 \log (x)+\frac {1}{4} (1+2 c_1) x^2+c_2 \]