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？

十分感谢 自己做的结果是y=2arctane^x^2+c
终于的了点分，提高

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))

Answer 2

dy/dx=2xsiny
dy/siny=2xdx
sinydy/(1-cosy^2)=2xdx
(1/2)ln[(1+cosy)/(1-cosy)]=-x^2+C0
ln(1+cosy)/siny=-x^2+C0
cot (y/2)=C1e^(-x^2)