Internal problem ID [5065]
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.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {y^{\prime \prime }+x \left (1-x \right ) y^{\prime }+y \,{\mathrm e}^{x}=0} \end {gather*}
✗ 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: 0.0 (sec). Leaf size: 0
DSolve[y''[x]+x*(1-x)*y'[x]+Exp[x]*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
Not solved