Internal problem ID [8678]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 2, linear second order
Problem number: 1098.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_Emden, _Fowler], [_2nd_order, _linear, _with_symmetry_[0,F(x)]]]
Solve \begin {gather*} \boxed {x y^{\prime \prime }-y^{\prime }-y a \,x^{3}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 27
dsolve(x*diff(diff(y(x),x),x)-diff(y(x),x)-y(x)*a*x^3=0,y(x), singsol=all)
\[ y \relax (x ) = c_{1} \sinh \left (\frac {x^{2} \sqrt {a}}{2}\right )+c_{2} \cosh \left (\frac {x^{2} \sqrt {a}}{2}\right ) \]
✓ Solution by Mathematica
Time used: 0.005 (sec). Leaf size: 41
DSolve[-(a*x^3*y[x]) - y'[x] + x*y''[x] == 0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to c_1 \cosh \left (\frac {\sqrt {a} x^2}{2}\right )+i c_2 \sinh \left (\frac {\sqrt {a} x^2}{2}\right ) \\ \end{align*}