Internal problem ID [8988]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 2, linear second order
Problem number: 1409.
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 {y^{\prime \prime }+a \,x^{-1+2 a} x^{-2 a} y^{\prime }+b^{2} x^{-2 a} y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.002 (sec). Leaf size: 39
dsolve(diff(diff(y(x),x),x) = -a*x^(2*a-1)/(x^(2*a))*diff(y(x),x)-b^2/(x^(2*a))*y(x),y(x), singsol=all)
\[ y \relax (x ) = c_{1} \sin \left (\frac {x^{-a +1} b}{a -1}\right )+c_{2} \cos \left (\frac {x^{-a +1} b}{a -1}\right ) \]
✓ Solution by Mathematica
Time used: 0.012 (sec). Leaf size: 44
DSolve[y''[x] == -((b^2*y[x])/x^(2*a)) - (a*y'[x])/x,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to c_1 \cos \left (\frac {b x^{1-a}}{a-1}\right )+c_2 \sin \left (\frac {b x^{1-a}}{1-a}\right ) \\ \end{align*}