Internal problem ID [4557]
Book: Basic Training in Mathematics. By R. Shankar. Plenum Press. NY. 1995
Section: Chapter 10, Differential equations. Section 10.4, ODEs with variable Coefficients. Second
order and Homogeneous. page 318
Problem number: 10.4.8 (b).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _exact, _linear, _homogeneous]]
Solve \begin {gather*} \boxed {x \left (1-x \right ) y^{\prime \prime }+2 \left (1-2 x \right ) y^{\prime }-2 y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 18
dsolve(x*(1-x)*diff(y(x),x$2)+2*(1-2*x)*diff(y(x),x)-2*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = \frac {c_{1} x +c_{2}}{\left (x -1\right ) x} \]
✓ Solution by Mathematica
Time used: 0.019 (sec). Leaf size: 22
DSolve[x*(1-x)*y''[x]+2*(1-2*x)*y'[x]-2*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {c_2 x+c_1}{x-x^2} \\ \end{align*}