Internal problem ID [5112]
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]
\[ \boxed {\left (-x^{2}+1\right ) y^{\prime }-y x=1} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 48
dsolve((1-x^2)*diff(y(x),x)=1+x*y(x),y(x), singsol=all)
\[ y \left (x \right ) = -\frac {\sqrt {\left (x -1\right ) \left (x +1\right )}\, \ln \left (x +\sqrt {x^{2}-1}\right )}{\left (x -1\right ) \left (x +1\right )}+\frac {c_{1}}{\sqrt {x -1}\, \sqrt {x +1}} \]
✓ Solution by Mathematica
Time used: 0.032 (sec). Leaf size: 54
DSolve[(1-x^2)*y'[x]==1+x*y[x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {\log \left (1-\frac {x}{\sqrt {x^2-1}}\right )-\log \left (\frac {x}{\sqrt {x^2-1}}+1\right )+2 c_1}{2 \sqrt {x^2-1}} \]