Question

麻烦高手帮忙看下这高数题,微分方程dy/dx=2xsiny的通解为多少?

Answer 1

dy/dx = 2xsiny

dy/siny = 2xdx

Ln(cscy-coty) = x² + C1 或者写为 Ln(tan(y/2)) = x² + C1

tan(y/2) = Ce^(x²) 或者写为 y = 2artan(Ce^(x²))