x-y的平方+e的xy次方=0隐函数的一阶二阶导数是多少

Question

x-y的平方+e的xy次方=0隐函数的一阶二阶导数是多少

Answer 1

(x-y)^2 + e^(xy) = 0 (1)
2(x-y)(1-y') + e^(xy)(y+xy') = 0 (2)
2(x-y)-2(x-y)y' + ye^(xy) + xe^(xy)y' = 0 (3)
y'[xe^(xy)-2(x-y)] = 2(y-x)-ye^(xy) y'= [2(y-x)-ye^(xy)]/[xe^(xy)-2(x-y)] (4)
由（3）：2(1-y')-2[(1-y')y'+(x-y)y"]+y'e^(xy)+ye^(xy)(y+xy')+y'e^(xy)(1+xy+x^2y')+xy"e^(xy)=0 (5')
y" [xe^(xy)-2(x-y)]+2(1-y')^2 +e^(xy){y'+y(y+xy')+y'(1+xy+x^2y')}=0
解出：y" = [-2(1-y')^2 -e^(xy){y'+y(y+xy')+y'(1+xy+x^2y')}]/ [xe^(xy)-2(x-y)] (5)