The order and degree of the differential equa | vedclass

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Question

(A) Given differential equation is $3 - (\frac{d^3 y}{d x^3})^{\frac{7}{3}} = (\frac{dy}{d x})^5$. To find the degree,we must eliminate the fractional

Vedclass · Accepted Answer

Order = $3$,Degree = $7$

Vedclass · Answer

(A) Given differential equation is $3 - (\frac{d^3 y}{d x^3})^{\frac{7}{3}} = (\frac{dy}{d x})^5$. To find the degree,we must eliminate the fractional exponent. Rearrange the equation: $3 - (\frac{dy}{d x})^5 = (\frac{d^3 y}{d x^3})^{\frac{7}{3}}$. Raise both sides to the power of $3$: $(3 - (\frac{dy}{d x})^5)^3 = (\frac{d^3 y}{d x^3})^7$. The highest order derivative present is $\frac{d^3 y}{d x^3}$,so the order is $3$. The power of the highest order derivative after making the equation free from radicals and fractions is $7$,so the degree is $7$.

The order and degree of the differential equation $3 - (\frac{d^3 y}{d x^3})^{\frac{7}{3}} = (\frac{dy}{d x})^5$ are respectively:

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