Internal problem ID [5431]
Book: Schaums Outline. Theory and problems of Differential Equations, 1st edition. Frank Ayres.
McGraw Hill 1952
Section: Chapter 19. Linear equations with variable coefficients (Misc. types). Supplemetary
problems. Page 132
Problem number: 24.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_y]]
\[ \boxed {x y^{\prime \prime }-y^{\prime }=-\frac {2}{x}-\ln \left (x \right )} \]
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 18
dsolve(x*diff(y(x),x$2)-diff(y(x),x)=-2/x-ln(x),y(x), singsol=all)
\[ y \left (x \right ) = \frac {c_{1} x^{2}}{2}+\ln \left (x \right ) x +\ln \left (x \right )+c_{2} \]
✓ Solution by Mathematica
Time used: 0.037 (sec). Leaf size: 23
DSolve[x*y''[x]-y'[x]==-2/x-Log[x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {c_1 x^2}{2}+(x+1) \log (x)+c_2 \]