Internal problem ID [4457]
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.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_linear]
Solve \begin {gather*} \boxed {\left (-x^{2}+1\right ) y^{\prime }-y x^{2}-\left (1+x \right ) \sqrt {-x^{2}+1}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.001 (sec). Leaf size: 34
dsolve((1-x^2)*diff(y(x),x)-x^2*y(x)=(1+x)*sqrt(1-x^2),y(x), singsol=all)
\[ y \relax (x ) = \frac {x +1}{\sqrt {-x^{2}+1}}+\frac {{\mathrm e}^{-x} \sqrt {x +1}\, c_{1}}{\sqrt {x -1}} \]
✓ Solution by Mathematica
Time used: 0.082 (sec). Leaf size: 33
DSolve[(1-x^2)*y'[x]-x^2*y[x]==(1+x)*Sqrt[1-x^2],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {e^{-x} \sqrt {x+1} \left (e^x+c_1\right )}{\sqrt {1-x}} \\ \end{align*}