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The degree and order of the differential equation $\left[1+\left(\frac{d y}{d x}\right)^{3}\right]^{7 / 3}=7\left(\frac{d^{2} y}{d x^{2}}\right)$ respectively are A) 3 and 7 B) 3 and 2 C) 7 and 3 D) 2 and 3
The degree and order of the differential equation $\left[1+\left(\frac{d y}{d x}\right)^{3}\right]^{7 / 3}=7\left(\frac{d^{2} y}{d x^{2}}\right)$ respectively are
A) 3 and 7
B) 3 and 2
C) 7 and 3
D) 2 and 3
Maths
The degree and order of the differential equation $\left[1+\left(\frac{d y}{d x}\right)^{3}\right]^{7 / 3}=7\left(\frac{d^{2} y}{d x^{2}}\right)$ respectively are
A) 3 and 7
B) 3 and 2
C) 7 and 3
D) 2 and 3

Solution:

Correct option is
(B) 3 and 2
Firstly we need to raise both eq. with power of 3 to make all the powers, integer, we obtain
$\left[1+\left(\frac{\mathrm{dy}}{\mathrm{dx}}\right)^{\frac{3}{3}}\right]^{7}=7\left(\frac{\mathrm{d}^{2} \mathrm{y}}{\mathrm{dx}^{2}}\right)^{3}$
The degree of a differential eq. is represented by the power of the highest order derivative in the given differential eq.. So here the degree is 3 . Order of a differential eq. is the order of the highest order derivative present in the eq. So here the order is 2 .

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