Internal problem ID [3038]
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]
\[ \boxed {\left (1-x^{2}\right ) y^{\prime }+\cos \left (x \right )-2 y x=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 19
dsolve((-x^2+1)*diff(y(x),x)+cos(x) = 2*x*y(x),y(x), singsol=all)
\[ y \left (x \right ) = \frac {c_{1} +\sin \left (x \right )}{\left (x -1\right ) \left (x +1\right )} \]
✓ Solution by Mathematica
Time used: 0.037 (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*}