Internal problem ID [4574]
Book: Engineering Mathematics. By K. A. Stroud. 5th edition. Industrial press Inc. NY.
2001
Section: Program 24. First order differential equations. Test excercise 24. page 1067
Problem number: 8.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {\left (x^{2}-1\right ) y^{\prime }+2 y x -x=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 22
dsolve((x^2-1)*diff(y(x),x)+2*x*y(x)=x,y(x), singsol=all)
\[ y \relax (x ) = \frac {\frac {x^{2}}{2}+c_{1}}{\left (x -1\right ) \left (x +1\right )} \]
✓ Solution by Mathematica
Time used: 0.047 (sec). Leaf size: 31
DSolve[(x^2-1)*y'[x]+2*x*y[x]==x,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {x^2+2 c_1}{2 \left (x^2-1\right )} \\ y(x)\to \frac {1}{2} \\ \end{align*}