Internal problem ID [4622]
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: 44.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_linear]
Solve \begin {gather*} \boxed {y^{\prime }+\left (\frac {1}{x}-\frac {2 x}{-x^{2}+1}\right ) y-\frac {1}{-x^{2}+1}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.002 (sec). Leaf size: 22
dsolve(diff(y(x),x)+(1/x-(2*x)/(1-x^2))*y(x)=1/(1-x^2),y(x), singsol=all)
\[ y \relax (x ) = \frac {-\frac {x^{2}}{2}+c_{1}}{x \left (x^{2}-1\right )} \]
✓ Solution by Mathematica
Time used: 0.039 (sec). Leaf size: 25
DSolve[y'[x]+(1/x-(2*x)/(1-x^2))*y[x]==1/(1-x^2),y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {x^2+2 c_1}{2 x-2 x^3} \\ \end{align*}