59.1.754 problem 776

Internal problem ID [9926]
Book : Collection of Kovacic problems
Section : section 1
Problem number : 776
Date solved : Monday, January 27, 2025 at 06:15:50 PM
CAS classification : [[_Emden, _Fowler]]

\begin{align*} x^{4} y^{\prime \prime }+\lambda y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.008 (sec). Leaf size: 31

dsolve(x^4*diff(y(x),x$2)+lambda*y(x)=0,y(x), singsol=all)
 

\[ y = x \left (c_{1} \sinh \left (\frac {\sqrt {-\lambda }}{x}\right )+c_{2} \cosh \left (\frac {\sqrt {-\lambda }}{x}\right )\right ) \]

✓ Solution by Mathematica

Time used: 0.108 (sec). Leaf size: 56

DSolve[x^4*D[y[x],{x,2}]+\[Lambda]*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to c_1 x e^{-1+\frac {i \sqrt {\lambda }}{x}}-\frac {i c_2 x e^{1-\frac {i \sqrt {\lambda }}{x}}}{2 \sqrt {\lambda }} \]