47.4.9 problem 57

Internal problem ID [7486]
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 : 57
Date solved : Monday, January 27, 2025 at 03:02:01 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }+x \left (1-x \right ) y^{\prime }+{\mathrm e}^{x} y&=0 \end{align*}

✗ Solution by Maple

dsolve(diff(y(x),x$2)+x*(1-x)*diff(y(x),x)+exp(x)*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,2}]+x*(1-x)*D[y[x],x]+Exp[x]*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

Not solved