7.21 problem 26

Internal problem ID [4351]

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.
ODE order: 2.
ODE degree: 1.

CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]

Solve \begin {gather*} \boxed {\left (x^{2}+1\right ) y^{\prime \prime }-2 y^{\prime } x +2 y=0} \end {gather*} Given that one solution of the ode is \begin {align*} y_1 &= x \end {align*}

Solution by Maple

Time used: 0.016 (sec). Leaf size: 15

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

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

Solution by Mathematica

Time used: 0.029 (sec). Leaf size: 21

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

\begin{align*} y(x)\to c_2 x-c_1 (x-i)^2 \\ \end{align*}