61.32.1 problem 211

Internal problem ID [12711]
Book : Handbook of exact solutions for ordinary differential equations. By Polyanin and Zaitsev. Second edition
Section : Chapter 2, Second-Order Differential Equations. section 2.1.2-7
Problem number : 211
Date solved : Tuesday, January 28, 2025 at 04:16:17 AM
CAS classification : [[_Emden, _Fowler]]

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

✓ Solution by Maple

Time used: 0.009 (sec). Leaf size: 31

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

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

✓ Solution by Mathematica

Time used: 0.144 (sec). Leaf size: 56

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

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