10.25 problem 291

Internal problem ID [3039]

Book: Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section: Various 10
Problem number: 291.
ODE order: 1.
ODE degree: 1.

CAS Maple gives this as type [_linear]

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

Solution by Maple

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

dsolve((-x^2+1)*diff(y(x),x)+cos(x) = 2*x*y(x),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: 0.043 (sec). Leaf size: 18

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

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