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What are the order and degree, respectively of the differential
equation $\left(\frac{\mathrm{d}^{2} \mathrm{y}}{\mathrm{dx}^{2}}\right)^{5 / 6}=\left(\frac{\mathrm{dy}}{\mathrm{dx}}\right)^{1 / 3} ?$3
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equation $\left(\frac{\mathrm{d}^{2} \mathrm{y}}{\mathrm{dx}^{2}}\right)^{5 / 6}=\left(\frac{\mathrm{dy}}{\mathrm{dx}}\right)^{1 / 3} ?$3
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The correct answer is:
2,5
Given differential equation is:
$\left(\frac{\mathrm{d}^{2} \mathrm{y}}{\mathrm{d} \mathrm{x}^{2}}\right)^{5 / 6}=\left(\frac{\mathrm{dy}}{\mathrm{dx}}\right)^{1 / 3}$
Raising both the side to power of 6 , to make it a polynomial of derivatives.
$\Rightarrow\left(\frac{\mathrm{d}^{2} \mathrm{y}}{\mathrm{dx}^{2}}\right)^{5}=\left(\frac{\mathrm{dy}}{\mathrm{dx}}\right)^{6 / 3} \Rightarrow\left(\frac{\mathrm{d}^{2} \mathrm{y}}{\mathrm{d} \mathrm{x}^{2}}\right)^{5}=\left(\frac{\mathrm{dy}}{\mathrm{dx}}\right)^{2}$
Highest derivative has power of $5 .$ So, the order and degree of given differential equation are 2 and 5 respectively.
$\left(\frac{\mathrm{d}^{2} \mathrm{y}}{\mathrm{d} \mathrm{x}^{2}}\right)^{5 / 6}=\left(\frac{\mathrm{dy}}{\mathrm{dx}}\right)^{1 / 3}$
Raising both the side to power of 6 , to make it a polynomial of derivatives.
$\Rightarrow\left(\frac{\mathrm{d}^{2} \mathrm{y}}{\mathrm{dx}^{2}}\right)^{5}=\left(\frac{\mathrm{dy}}{\mathrm{dx}}\right)^{6 / 3} \Rightarrow\left(\frac{\mathrm{d}^{2} \mathrm{y}}{\mathrm{d} \mathrm{x}^{2}}\right)^{5}=\left(\frac{\mathrm{dy}}{\mathrm{dx}}\right)^{2}$
Highest derivative has power of $5 .$ So, the order and degree of given differential equation are 2 and 5 respectively.
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