Internal problem ID [10930]
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 20(d).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {\left (x^{2}-x \right ) y^{\prime \prime }+\left (2 x^{2}+4 x -3\right ) y^{\prime }+8 x y=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 26
dsolve((x^2-x)*diff(y(x),x$2)+(2*x^2+4*x-3)*diff(y(x),x)+8*x*y(x)=0,y(x), singsol=all)
\[ y \left (x \right ) = \frac {c_{1}}{x^{2} \left (x -1\right )^{2}}+\frac {c_{2} {\mathrm e}^{-2 x}}{\left (x -1\right )^{2}} \]
✓ Solution by Mathematica
Time used: 0.042 (sec). Leaf size: 30
DSolve[(x^2-x)*y''[x]+(2*x^2+4*x-3)*y'[x]+8*x*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {\frac {2 c_1}{x^2}+c_2 e^{-2 x}}{2 (x-1)^2} \\ \end{align*}