Internal problem ID [11045]
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 Equation of form
\((a_4 x^4+a_3 x^3+a_2 x^2 x+a_1 x+a_0) y''+f(x)y'+g(x)y=0\)
Problem number: 211.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_Emden, _Fowler]]
\[ \boxed {x^{4} y^{\prime \prime }+a y=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 31
dsolve(x^4*diff(y(x),x$2)+a*y(x)=0,y(x), singsol=all)
\[ y \left (x \right ) = c_{1} x \sinh \left (\frac {\sqrt {-a}}{x}\right )+c_{2} x \cosh \left (\frac {\sqrt {-a}}{x}\right ) \]
✓ Solution by Mathematica
Time used: 0.199 (sec). Leaf size: 52
DSolve[x^4*y''[x]+a*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to c_1 x e^{\frac {i \sqrt {a}}{x}}-\frac {i c_2 x e^{-\frac {i \sqrt {a}}{x}}}{2 \sqrt {a}} \]