Internal problem ID [8980]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 2, linear second order
Problem number: 1401.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {y^{\prime \prime }+\frac {\left (3 x^{2}+a \right ) y^{\prime }}{x^{3}}+\frac {b y}{x^{6}}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 45
dsolve(diff(diff(y(x),x),x) = -1/x^3*(3*x^2+a)*diff(y(x),x)-b/x^6*y(x),y(x), singsol=all)
\[ y \relax (x ) = c_{1} {\mathrm e}^{-\frac {-a +\sqrt {a^{2}-4 b}}{4 x^{2}}}+c_{2} {\mathrm e}^{\frac {a +\sqrt {a^{2}-4 b}}{4 x^{2}}} \]
✓ Solution by Mathematica
Time used: 0.007 (sec). Leaf size: 56
DSolve[y''[x] == -((b*y[x])/x^6) - ((a + 3*x^2)*y'[x])/x^3,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to e^{\frac {a-\sqrt {a^2-4 b}}{4 x^2}} \left (c_1 e^{\frac {\sqrt {a^2-4 b}}{2 x^2}}+c_2\right ) \\ \end{align*}