37.3.2 problem 10.4.8 (b)

Internal problem ID [6408]
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)
Date solved : Monday, January 27, 2025 at 02:00:50 PM
CAS classification : [[_2nd_order, _exact, _linear, _homogeneous]]

\begin{align*} x \left (1-x \right ) y^{\prime \prime }+2 \left (1-2 x \right ) y^{\prime }-2 y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.000 (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)
 

\[ y = \frac {c_1 x +c_2}{\left (x -1\right ) x} \]

✓ Solution by Mathematica

Time used: 0.037 (sec). Leaf size: 22

DSolve[x*(1-x)*D[y[x],{x,2}]+2*(1-2*x)*D[y[x],x]-2*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {c_2 x+c_1}{x-x^2} \]