Internal problem ID [8924]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 2, linear second order
Problem number: 1345.
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 {y^{\prime }}{x^{3}}-\frac {2 y}{x^{4}}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.005 (sec). Leaf size: 32
dsolve(diff(diff(y(x),x),x) = -1/x^3*diff(y(x),x)+2/x^4*y(x),y(x), singsol=all)
\[ y \relax (x ) = c_{1} x \,{\mathrm e}^{\frac {1}{2 x^{2}}}+c_{2} x \,{\mathrm e}^{\frac {1}{2 x^{2}}} \erf \left (\frac {\sqrt {2}}{2 x}\right ) \]
✓ Solution by Mathematica
Time used: 0.041 (sec). Leaf size: 45
DSolve[y''[x] == (2*y[x])/x^4 - y'[x]/x^3,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{2} e^{\frac {1}{2 x^2}} x \left (2 c_1-\sqrt {2 \pi } c_2 \text {Erf}\left (\frac {1}{\sqrt {2} x}\right )\right ) \\ \end{align*}