47.4.8 problem 56

Internal problem ID [7485]
Book : Ordinary differential equations and calculus of variations. Makarets and Reshetnyak. Wold Scientific. Singapore. 1995
Section : Chapter 2. Linear homogeneous equations. Section 2.2 problems. page 95
Problem number : 56
Date solved : Monday, January 27, 2025 at 03:02:01 PM
CAS classification : [[_3rd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime \prime }-2 x y^{\prime \prime }+4 x^{2} y^{\prime }+8 x^{3} y&=0 \end{align*}

✗ Solution by Maple

dsolve(diff(y(x),x$3)-2*x*diff(y(x),x$2)+4*x^2*diff(y(x),x)+8*x^3*y(x)=0,y(x), singsol=all)
 

\[ \text {No solution found} \]

✗ Solution by Mathematica

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

DSolve[D[y[x],{x,3}]-2*x*D[y[x],{x,2}]+4*x^2*D[y[x],x]+8*x^3*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

Not solved