Internal problem ID [10906]
Book: APPLIED DIFFERENTIAL EQUATIONS The Primary Course by Vladimir A. Dobrushkin.
CRC Press 2015
Section: Chapter 4, Second and Higher Order Linear Differential Equations. Problems page
221
Problem number: Problem 10.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {\left (x -1\right ) y^{\prime \prime }-y^{\prime } x +y=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 12
dsolve((x-1)*diff(y(x),x$2)-x*diff(y(x),x)+y(x)=0,y(x), singsol=all)
\[ y \left (x \right ) = c_{1} x +c_{2} {\mathrm e}^{x} \]
✓ Solution by Mathematica
Time used: 0.013 (sec). Leaf size: 17
DSolve[(x-1)*y''[x]-x*y'[x]+y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to c_1 e^x-c_2 x \\ \end{align*}