36.2.16 problem 16

Internal problem ID [6309]
Book : Fundamentals of Differential Equations. By Nagle, Saff and Snider. 9th edition. Boston. Pearson 2018.
Section : Chapter 2, First order differential equations. Section 2.3, Linear equations. Exercises. page 54
Problem number : 16
Date solved : Monday, January 27, 2025 at 01:55:44 PM
CAS classification : [_linear]

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

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 52

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

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

✓ Solution by Mathematica

Time used: 0.088 (sec). Leaf size: 33

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

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