38.2.26 problem 26

Internal problem ID [6455]
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
Date solved : Monday, January 27, 2025 at 02:04:37 PM
CAS classification : [_linear]

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

✓ Solution by Maple

Time used: 0.000 (sec). Leaf size: 46

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

\[ y = -\frac {\sqrt {x^{2}-1}\, \ln \left (x +\sqrt {x^{2}-1}\right )}{\left (x -1\right ) \left (x +1\right )}+\frac {c_1}{\sqrt {x -1}\, \sqrt {x +1}} \]

✓ Solution by Mathematica

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

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

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