Internal problem ID [10808]
Book: Differential equations and the calculus of variations by L. ElSGOLTS. MIR PUBLISHERS,
MOSCOW, Third printing 1977.
Section: Chapter 1, First-Order Differential Equations. Problems page 88
Problem number: Problem 59.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_linear]
\[ \boxed {\left (x^{2}-1\right ) y^{\prime }+2 x y-\cos \left (x \right )=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 19
dsolve((x^2-1)*diff(y(x),x)+2*x*y(x)-cos(x)=0,y(x), singsol=all)
\[ y \left (x \right ) = \frac {\sin \left (x \right )+c_{1}}{\left (x -1\right ) \left (x +1\right )} \]
✓ Solution by Mathematica
Time used: 0.042 (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*}