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

$$\frac{d^{2}y}{{dx}^2}=\frac{cy}{x^2}$$$$y\left(x\right)=?$$

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

$$y={kx}^n$$$$y^{″}=kn(n-1)x^{n-2}={ckx}^{n-2}$$$$n(n-1)=c$$$$n^2-n-c=0$$$$n=\frac{1\pm \sqrt{1+4\mathrm{c}}}{2}$$$$y=c_1{x}^{\frac{1+\sqrt{1+4c}}{2}}+c_2{x}^{\frac{1-\sqrt{1+4c}}{2}}$$

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