Internal problem ID [7061]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 332.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_Emden, _Fowler]]
Solve \begin {gather*} \boxed {x^{4} y^{\prime \prime }+\lambda y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 31
dsolve(x^4*diff(y(x),x$2)+lambda*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = c_{1} x \sinh \left (\frac {\sqrt {-\lambda }}{x}\right )+c_{2} x \cosh \left (\frac {\sqrt {-\lambda }}{x}\right ) \]
✓ Solution by Mathematica
Time used: 0.095 (sec). Leaf size: 52
DSolve[x^4*y''[x]+\[Lambda]*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to c_1 x e^{\frac {i \sqrt {\lambda }}{x}}-\frac {i c_2 x e^{-\frac {i \sqrt {\lambda }}{x}}}{2 \sqrt {\lambda }} \\ \end{align*}