61.32.2 problem 212

Internal problem ID [12712]
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 : 212
Date solved : Tuesday, January 28, 2025 at 08:23:47 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} x^{4} y^{\prime \prime }+\left (a \,x^{2}+b x +c \right ) y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.276 (sec). Leaf size: 59

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

\[ y = x \left (c_{1} \operatorname {WhittakerM}\left (-\frac {i b}{2 \sqrt {c}}, \frac {\sqrt {-4 a +1}}{2}, \frac {2 i \sqrt {c}}{x}\right )+c_{2} \operatorname {WhittakerW}\left (-\frac {i b}{2 \sqrt {c}}, \frac {\sqrt {-4 a +1}}{2}, \frac {2 i \sqrt {c}}{x}\right )\right ) \]

✗ Solution by Mathematica

Time used: 0.000 (sec). Leaf size: 0

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

Not solved