d-2-y-dx-2-cy-x-2-y-x-

Question Number 1964 by 123456 last updated on 26/Oct/15

\frac{d^{2} y}{{d x}^{2}} = \frac{c y}{x^{2}}

y (x) = ?

Answered by prakash jain last updated on 26/Oct/15

y = {k x}^{n}

y^{″} = k n (n - 1) x^{n - 2} = {c k x}^{n - 2}

n (n - 1) = c

n^{2} - n - c = 0

n = \frac{1 \pm \sqrt{1 + 4 c}}{2}

y = c_{1} x^{\frac{1 + \sqrt{1 + 4 c}}{2}} + c_{2} x^{\frac{1 - \sqrt{1 + 4 c}}{2}}