Internal problem ID [8762]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 2, linear second order
Problem number: 1182.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {x^{2} y^{\prime \prime }-3 x y^{\prime }+4 y-5 x=0} \end {gather*}
✓ Solution by Maple
Time used: 0.005 (sec). Leaf size: 20
dsolve(x^2*diff(diff(y(x),x),x)-3*x*diff(y(x),x)+4*y(x)-5*x=0,y(x), singsol=all)
\[ y \relax (x ) = c_{2} x^{2}+x^{2} \ln \relax (x ) c_{1}+5 x \]
✓ Solution by Mathematica
Time used: 0.01 (sec). Leaf size: 20
DSolve[-5*x + 4*y[x] - 3*x*y'[x] + x^2*y''[x] == 0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to x (c_1 x+2 c_2 x \log (x)+5) \\ \end{align*}