If a and b are respectively the order and deg | vedclass

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(C) Given the differential equation: $y^2(y^{\prime \prime})^2 + 3x(y^{\prime})^{1/3} + x^2y^2 = \sin x$. To find the degree,we must eliminate the fra

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$b = 3a$

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(C) Given the differential equation: $y^2(y^{\prime \prime})^2 + 3x(y^{\prime})^{1/3} + x^2y^2 = \sin x$. To find the degree,we must eliminate the fractional exponent of the derivative. Rearranging the equation: $y^2(y^{\prime \prime})^2 + x^2y^2 - \sin x = -3x(y^{\prime})^{1/3}$. Cubing both sides to remove the power of $1/3$: $(y^2(y^{\prime \prime})^2 + x^2y^2 - \sin x)^3 = (-3x)^3(y^{\prime}) = -27x^3(y^{\prime})$. The highest order derivative present is $y^{\prime \prime}$,so the order $a = 2$. The highest power of the highest order derivative after making the equation a polynomial in derivatives is $2 	imes 3 = 6$. Thus,the degree $b = 6$. Comparing $a = 2$ and $b = 6$,we get $b = 3a$.

If $a$ and $b$ are respectively the order and degree of the differential equation $y^2(y^{\prime \prime})^2 + 3x(y^{\prime})^{1/3} + x^2y^2 = \sin x$,then:

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