(1)(x^2-2y^2)dx+xydy=0的通解 (2)(1+2e^x/y)dx+2e^x/y(1-x/y)dy=0的通解

(1)dy/dx=2y/x-x/y设y/x=u,y=ux,则dy/dx=u'x+u得u'x+u=2u-1/udu/dx=(u-1/u)/x即udu/(u^2-1)=dx/x1/2ln|u^2-1|=ln|x|+C0所以通解为(y/x)^2-1=Cx^2(2)dx/dy=2e^(x/y)(x/y-1)/(1+2e^(x/y))设x/y=u,dx/dy=u'y+uu'y+u=2e^...