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  4. The order and degree of the differential equation √(d y/d x)-4 (d y/d x)-7 x=0 are

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Q. The order and degree of the differential equation $\sqrt{\frac{d y}{d x}}-4 \frac{d y}{d x}-7 x=0$ are

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Solution:

Given equation is $\sqrt{\frac{d y}{d x}}-4 \frac{d y}{d x}-7 x=0$
$\Rightarrow \frac{d y}{d x}=16\left(\frac{d y}{d x}\right)^2+49 x^2+56 x \frac{d y}{d x}$
Obviously, it is of first order and second degree differential equation.