Question

求此方程所确定的二阶导数

Answer 1

x = acost...............(1)
y = bsint...............(2)
(bx)²+(ay)² = (ab)² cos²t + (ab)² sin²t = a²b²............(3)
x²/a² + y²/b² = 1.............(4)...............(椭圆方程)
x/a² + yy'/b² = 0.............(5)...............(对 x求导)
b²x + a²yy' = 0...............(6)
解出：
y' = dy/dx = -b²x/a²y...................(7)
(6)再对 x求导一次：
b² + a²(y'² + yy'') = 0..................(8)
解出：
y'' = d²y/dx² = -(b²+a²y'²)/a²y...................................(9)
将(7)代入(9)，即为所求。