35.4.13 problem 13

Internal problem ID [6131]
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
Date solved : Monday, January 27, 2025 at 01:37:55 PM
CAS classification : [_linear]

\begin{align*} \left (x -1\right ) y^{\prime }+y-\frac {1}{x^{2}}+\frac {2}{x^{3}}&=0 \end{align*}

✓ 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)
 

\[ y = \frac {c_1}{x -1}-\frac {1}{x^{2}} \]

✓ Solution by Mathematica

Time used: 0.043 (sec). Leaf size: 24

DSolve[(x-1)*D[y[x],x]+y[x]-1/x^2+2/x^3==0,y[x],x,IncludeSingularSolutions -> True]
 

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