Internal problem ID [8765]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 2, linear second order
Problem number: 1185.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {y^{\prime \prime } x^{2}+5 x y^{\prime }-\left (2 x^{3}-4\right ) y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 35
dsolve(x^2*diff(diff(y(x),x),x)+5*x*diff(y(x),x)-(2*x^3-4)*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = \frac {c_{1} \BesselI \left (0, \frac {2 \sqrt {2}\, x^{\frac {3}{2}}}{3}\right )}{x^{2}}+\frac {c_{2} \BesselK \left (0, \frac {2 \sqrt {2}\, x^{\frac {3}{2}}}{3}\right )}{x^{2}} \]
✓ Solution by Mathematica
Time used: 0.02 (sec). Leaf size: 56
DSolve[(4 - 2*x^3)*y[x] + 5*x*y'[x] + x^2*y''[x] == 0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {6 \sqrt [3]{6} c_2 K_0\left (\frac {2}{3} \sqrt {2} x^{3/2}\right )-3 \sqrt [3]{-6} c_1 \, _0\tilde {F}_1\left (;1;\frac {2 x^3}{9}\right )}{2 x^2} \\ \end{align*}