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Form the differential equations of the following families of curves by elimnating the parameters (arbitrary constants) given against them in the brackets. (i) y = c(x-c)^(2), (c) (ii) xy = a e^(x) + b e^(-x), (a, b) (iii) y = (a+bx)e^(Kx), (a,b) (iv) y = a cos (nx + b), (a,b) (v) = y = a e^(3x) + be^(4x), (a,b) (vi) y = ax^(2) + bx, (a,b) (vii) ax^(2) + by^(2) = 1 (a,b) |
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Answer» (ii) `x(d^(2)y)/(dx^(2)) + 2(dy)/(dx) - xy = 0` (iii) `y_(2) - 2ky_(1) + k^(2)y = 0` (iv) `y_(2) + n^(2)y = 0` (V) `y_(2) - 7y_(1) + 12y = 0` (vi) `x^(2)(d^(2)y)/(dx^(2)) - 2X(dy)/(dx) + 2y = 0` (vii) `xy y_(2) + xy_(1)^(2) - y y_(1) = 0` |
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