32.6.32 problem Exercise 12.32, page 103

Internal problem ID [5897]
Book : Ordinary Differential Equations, By Tenenbaum and Pollard. Dover, NY 1963
Section : Chapter 2. Special types of differential equations of the first kind. Lesson 12, Miscellaneous Methods
Problem number : Exercise 12.32, page 103
Date solved : Monday, January 27, 2025 at 01:25:13 PM
CAS classification : [_linear]

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

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 16

dsolve((x^2-1)*diff(y(x),x)+2*x*y(x)-cos(x)=0,y(x), singsol=all)
 

\[ y \left (x \right ) = \frac {\sin \left (x \right )+c_{1}}{x^{2}-1} \]

✓ Solution by Mathematica

Time used: 0.039 (sec). Leaf size: 18

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

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