3.9 problem 9

Internal problem ID [4261]

Book: Mathematical Methods in the Physical Sciences. third edition. Mary L. Boas. John Wiley. 2006
Section: Chapter 8, Ordinary differential equations. Section 3. Linear First-Order Equations. page 403
Problem number: 9.
ODE order: 1.
ODE degree: 1.

CAS Maple gives this as type [_linear]

Solve \begin {gather*} \boxed {\left (1-x^{2}\right ) y^{\prime }-y x -2 x \sqrt {1-x^{2}}=0} \end {gather*}

Solution by Maple

Time used: 0.0 (sec). Leaf size: 30

dsolve((1-x^2)*diff(y(x),x)=x*y(x)+2*x*sqrt(1-x^2),y(x), singsol=all)
 

\[ y \relax (x ) = \frac {x^{2}}{\sqrt {-x^{2}+1}}+\frac {c_{1}}{\sqrt {x -1}\, \sqrt {x +1}} \]

Solution by Mathematica

Time used: 0.102 (sec). Leaf size: 33

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

\begin{align*} y(x)\to \frac {x^2}{\sqrt {1-x^2}}+\frac {c_1}{\sqrt {x^2-1}} \\ \end{align*}