Internal problem ID [4965]
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]
\[ \boxed {\left (-x^{2}+1\right ) y^{\prime }-y x^{2}=\left (x +1\right ) \sqrt {-x^{2}+1}} \]
✓ Solution by Maple
Time used: 0.0 (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)
\[ y \left (x \right ) = \frac {{\mathrm e}^{-x} \sqrt {1+x}\, c_{1} \sqrt {-x^{2}+1}+\sqrt {x -1}\, x +\sqrt {x -1}}{\sqrt {-x^{2}+1}\, \sqrt {x -1}} \]
✓ Solution by Mathematica
Time used: 0.085 (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]
\[ y(x)\to \frac {e^{-x} \sqrt {x+1} \left (e^x+c_1\right )}{\sqrt {1-x}} \]