35.7.21 problem 26

Internal problem ID [6203]
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 : 26
Date solved : Monday, January 27, 2025 at 01:47:40 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} \left (x^{2}+1\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: 0.004 (sec). Leaf size: 16

dsolve([(x^2+1)*diff(y(x),x$2)-2*x*diff(y(x),x)+2*y(x)=0,x],singsol=all)
 

\[ y = c_{2} x^{2}+c_{1} x -c_{2} \]

✓ Solution by Mathematica

Time used: 0.044 (sec). Leaf size: 21

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

\[ y(x)\to c_2 x-c_1 (x-i)^2 \]