Internal problem ID [8763]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 2, linear second order
Problem number: 1183.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _exact, _linear, _nonhomogeneous]]
Solve \begin {gather*} \boxed {x^{2} y^{\prime \prime }-3 x y^{\prime }-5 y-x^{2} \ln \relax (x )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.002 (sec). Leaf size: 22
dsolve(x^2*diff(diff(y(x),x),x)-3*x*diff(y(x),x)-5*y(x)-x^2*ln(x)=0,y(x), singsol=all)
\[ y \relax (x ) = x^{5} c_{2}-\frac {x^{2} \ln \relax (x )}{9}+\frac {c_{1}}{x} \]
✓ Solution by Mathematica
Time used: 0.008 (sec). Leaf size: 27
DSolve[-(x^2*Log[x]) - 5*y[x] - 3*x*y'[x] + x^2*y''[x] == 0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to c_2 x^5-\frac {1}{9} x^2 \log (x)+\frac {c_1}{x} \\ \end{align*}