Internal problem ID [4279]
Book: Mathematical Methods in the Physical Sciences. third edition. Mary L. Boas. John Wiley.
2006
Section: Chapter 8, Ordinary differential equations. Section 4. OTHER METHODS FOR
FIRST-ORDER EQUATIONS. page 406
Problem number: 13.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_linear]
Solve \begin {gather*} \boxed {\left (x -1\right ) y^{\prime }+y-\frac {1}{x^{2}}+\frac {2}{x^{3}}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.001 (sec). Leaf size: 17
dsolve((x-1)*diff(y(x),x)+y(x)-1/x^2+2/x^3=0,y(x), singsol=all)
\[ y \relax (x ) = \frac {c_{1}}{x -1}-\frac {1}{x^{2}} \]
✓ Solution by Mathematica
Time used: 0.036 (sec). Leaf size: 20
DSolve[(x-1)*y'[x]+y[x]-1/x^2+2/x^3==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {1}{x^2}-\frac {c_1}{x-1} \\ \end{align*}