35.7.20 problem 25

Internal problem ID [6202]
Book : Mathematical Methods in the Physical Sciences. third edition. Mary L. Boas. John Wiley. 2006
Section : Chapter 8, Ordinary differential equations. Section 7. Other second-Order equations. page 435
Problem number : 25
Date solved : Monday, January 27, 2025 at 01:47:39 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

Using reduction of order method given that one solution is

\begin{align*} y&=x \end{align*}

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 19

dsolve([x^2*(2-x)*diff(y(x),x$2)+2*x*diff(y(x),x)-2*y(x)=0,x],singsol=all)
 

\[ y = \frac {c_{1} x^{2}+c_{2} \left (x -1\right )}{x} \]

✓ Solution by Mathematica

Time used: 0.045 (sec). Leaf size: 24

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

\[ y(x)\to \frac {c_1 (x-2)^2+c_2 (x-1)}{x} \]