35.3.9 problem 9

Internal problem ID [6113]
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
Date solved : Monday, January 27, 2025 at 01:36:25 PM
CAS classification : [_linear]

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

✓ Solution by Maple

Time used: 0.002 (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)
 

\[ y = \frac {x^{2}}{\sqrt {-x^{2}+1}}+\frac {c_1}{\sqrt {x -1}\, \sqrt {x +1}} \]

✓ Solution by Mathematica

Time used: 0.064 (sec). Leaf size: 33

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

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