6.32 problem Exercise 12.32, page 103

Internal problem ID [4045]

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.
ODE order: 1.
ODE degree: 1.

CAS Maple gives this as type [_linear]

Solve \begin {gather*} \boxed {\left (x^{2}-1\right ) y^{\prime }+2 x y-\cos \relax (x )=0} \end {gather*}

Solution by Maple

Time used: 0.002 (sec). Leaf size: 19

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

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

Solution by Mathematica

Time used: 0.041 (sec). Leaf size: 18

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

\begin{align*} y(x)\to \frac {\sin (x)+c_1}{x^2-1} \\ \end{align*}