Internal problem ID [8983]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 2, linear second order
Problem number: 1404.
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 (2 x^{2}+1\right ) y^{\prime }}{x^{3}}+\frac {\left (-2 x^{2}+1\right ) y}{4 x^{6}}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 24
dsolve(diff(diff(y(x),x),x) = -(2*x^2+1)/x^3*diff(y(x),x)-1/4*(-2*x^2+1)/x^6*y(x),y(x), singsol=all)
\[ y \relax (x ) = c_{1} {\mathrm e}^{\frac {1}{4 x^{2}}}+\frac {c_{2} {\mathrm e}^{\frac {1}{4 x^{2}}}}{x} \]
✓ Solution by Mathematica
Time used: 0.011 (sec). Leaf size: 25
DSolve[y''[x] == -1/4*((1 - 2*x^2)*y[x])/x^6 - ((1 + 2*x^2)*y'[x])/x^3,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {e^{\frac {1}{4 x^2}} (c_2 x+c_1)}{x} \\ \end{align*}