66.1.45 problem Problem 59

Internal problem ID [13892]
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
Date solved : Tuesday, January 28, 2025 at 06:07:40 AM
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)
 

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

✓ Solution by Mathematica

Time used: 0.051 (sec). Leaf size: 18

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

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