解微分方程dx/dy=－x－y^2
问题描述：
解微分方程dx/dy=－x－y^2
答
x'+x=-y²(e^y)(x'+x)=-y²e^y[xe^y]'=-y²e^yxe^y=∫-y²e^ydy=-y²e^y+∫2ye^y=-y²e^y+2ye^y-∫2e^ydy=-y²e^y+2ye^y-2e^y+Cx=-y²+2y-2+Ce^(-y)
解微分方程dx/dy=－x－y^2
x'+x=-y²(e^y)(x'+x)=-y²e^y[xe^y]'=-y²e^yxe^y=∫-y²e^ydy=-y²e^y+∫2ye^y=-y²e^y+2ye^y-∫2e^ydy=-y²e^y+2ye^y-2e^y+Cx=-y²+2y-2+Ce^(-y)