2.26 problem 26

Internal problem ID [4604]

Book: Engineering Mathematics. By K. A. Stroud. 5th edition. Industrial press Inc. NY. 2001
Section: Program 24. First order differential equations. Further problems 24. page 1068
Problem number: 26.
ODE order: 1.
ODE degree: 1.

CAS Maple gives this as type [_linear]

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

Solution by Maple

Time used: 0.001 (sec). Leaf size: 48

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

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

Solution by Mathematica

Time used: 0.038 (sec). Leaf size: 32

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

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