Internal problem ID [11036]
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: 212.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {x^{4} y^{\prime \prime }+\left (a \,x^{2}+b x +c \right ) y=0} \]
✓ Solution by Maple
Time used: 0.125 (sec). Leaf size: 63
dsolve(x^4*diff(y(x),x$2)+(a*x^2+b*x+c)*y(x)=0,y(x), singsol=all)
\[ y \left (x \right ) = x \left (c_{1} \operatorname {WhittakerM}\left (-\frac {i b}{2 \sqrt {c}}, \frac {\sqrt {-4 a +1}}{2}, \frac {2 i \sqrt {c}}{x}\right )+c_{2} \operatorname {WhittakerW}\left (-\frac {i b}{2 \sqrt {c}}, \frac {\sqrt {-4 a +1}}{2}, \frac {2 i \sqrt {c}}{x}\right )\right ) \]
✗ Solution by Mathematica
Time used: 0.0 (sec). Leaf size: 0
DSolve[x^4*y''[x]+(a*x^2+b*x+c)*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
Not solved