38.1.8 problem 8

Internal problem ID [6425]
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
Date solved : Monday, January 27, 2025 at 02:02:34 PM
CAS classification : [_separable]

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

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 21

dsolve((x^2-1)*diff(y(x),x)+2*x*y(x)=x,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.032 (sec). Leaf size: 31

DSolve[(x^2-1)*D[y[x],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*}