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Question Number 53890 by shaddie last updated on 27/Jan/19

$$\mathrm{pls}.\mathrm{help}\mathrm{me}\mathrm{solve}\mathrm{this}$$$$\mathrm{if}\mathrm{y}=\frac{\mathrm{x}-2}{2\mathrm{x}-1}\mathrm{show}\mathrm{that}(2\mathrm{x}-1)\frac{{\mathrm{d}}^2\mathrm{y}}{{\mathrm{dx}}^2}+4\frac{\mathrm{dy}}{\mathrm{dx}}=0$$

Answered by math1967 last updated on 27/Jan/19

$$\Rightarrow y(2x-1)=(x-2)$$$$\Rightarrow 2y+(2x-1)\frac{dy}{dx}=1$$$$\Rightarrow 2\frac{dy}{dx}+2\frac{dy}{dx}+(2x-1)\frac{d^{2}y}{{dx}^2}=0$$$$\therefore (2x-1)\frac{d^{2}y}{{dx}^2}+4\frac{dy}{dx}=0$$

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