Question

已知y的导数=e∧xy,求函数y?

Answer 1

y' = e^(xy), 令 u = xy， 则 u' = y+xy',
y' = (u'-y)/x = (u'-u/x)/x = u, xu' - u = ux^2
xdu/dx = u(1+x^2), du/u = (1/x + x)dx
lnu = lnx + x^2/2 + lnC
u = Cxe^(x^2/2), 通解 y = Ce^(x^2/2)