The order and degree of the differential equa | vedclass

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Question

(C) Given the differential equation: $\frac{d^3 y}{d x^3} = \left[1 + \left(\frac{d y}{d x}\right)^2\right]^{5/2}$.To find the degree,we must eliminat

Vedclass · Accepted Answer

$3, 2$

Vedclass · Answer

(C) Given the differential equation: $\frac{d^3 y}{d x^3} = \left[1 + \left(\frac{d y}{d x}\right)^2\right]^{5/2}$.To find the degree,we must eliminate the fractional exponent by squaring both sides:$\left(\frac{d^3 y}{d x^3}\right)^2 = \left[1 + \left(\frac{d y}{d x}\right)^2\right]^5$.The order of a differential equation is the highest derivative present,which is $3$ (from $\frac{d^3 y}{d x^3}$).The degree is the power of the highest derivative after the equation is made free from radicals and fractions,which is $2$.Therefore,the order is $3$ and the degree is $2$.

The order and degree of the differential equation $\frac{d^3 y}{d x^3} = \left[1 + \left(\frac{d y}{d x}\right)^2\right]^{5/2}$ are respectively:

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