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For each of the differential equations given below, indicate its order and degree (if defined).(i) `(d^2y)/(dx^2)+5x((dy)/(dx))^2-6x y=logx` (ii) `((dy)/(dx))^3-4((dy)/(dx))^2+7y=sinx`(iii) `(d^4y)/(dx^4)-sin((d^3y)/(dx^3))=0`

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To determine the order and degree of the given differential equations, we will analyze each equation step by step. ### (i) \( \frac{d^2y}{dx^2} + 5x\left(\frac{dy}{dx}\right)^2 - 6xy = \log x \) 1. **Identify the highest derivative**: The highest derivative in this equation is \( \frac{d^2y}{dx^2} \), which is the second derivative of \( y \). **Order**: 2 ...
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