29.10.25 problem 291

Internal problem ID [4891]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 10
Problem number : 291
Date solved : Monday, January 27, 2025 at 09:46:39 AM
CAS classification : [_linear]

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

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 16

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

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

✓ Solution by Mathematica

Time used: 0.038 (sec). Leaf size: 18

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

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