Question

11和12 在线等大一高数数学分析微积分计算小题～感谢大神帮助！！…高分求各种解题～毛都不会也

11和12 在线等大一高数数学分析微积分计算小题～感谢大神帮助！！…高分求各种解题～毛都不会也是醉了…有余力的大神请戳我的提问哈！问了好多！欢迎回答，满意追加～

Answer 1

y^3 + xy^2 + x^2y + 64 = 0
两边求导：
3y^2y' + y^2 + 2xyy' + 2xy + x^2y' = 0
∴y' = -(y^2 + 2xy)/(3y^2 + 2xy + x^2)
y(0) = 4
y'(0) = -4^2/3*4^2 = -1/3

y" = [-(y^2 + 2xy)'(3y^2 + 2xy + x^2)+(y^2 + 2xy)(3y^2 + 2xy + x^2)']/(3y^2 + 2xy + x^2)^2
= [-(2yy'+2y+2xy')(3y^2 + 2xy + x^2)+(y^2 + 2xy)(6yy'+2y+2xy'+2x)]/(3y^2 + 2xy + x^2)^2
= [4xy^2y'+2x^2yy'-2x^3y'-4y^3-2xy^2+2x^2y]/(3y^2 + 2xy + x^2)^2
= [-6x^2y^3+6x^4y-12y^5-18xy^4-4xy^3+2x^2y^2]/(3y^2 + 2xy + x^2)^3
y“(0) = 0

答题不易，请及时采纳，谢谢！