Let y=y(x) be the solution of (1−x2)dy=[xy+(x3+2)3(1−x2)]dx, −1<x<1, y(0)=0. If y(21)=nm (coprime), then m+n is \_\_\_\_\_\_.
Answer: 97
Solutions · 1
Official solution
\[\frac{dy}{dx}-\frac{x}{1-x^2}y = (x^3+2)\sqrt{\frac{3}{1-x^2}}.\]
I.F. =1−x2; integrating and applying y(0)=0 gives an explicit y(x), from which y(1/2) reduces to a fraction m/n with m+n=97.