The sum of the degree and order of the differ | vedclass

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(C) Given differential equation is $(1+y_1^2)^{2/3} = y_2$. To find the degree,we need to eliminate the fractional exponent. Cube both sides of the eq

Vedclass · Accepted Answer

$5$

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(C) Given differential equation is $(1+y_1^2)^{2/3} = y_2$. To find the degree,we need to eliminate the fractional exponent. Cube both sides of the equation: $((1+y_1^2)^{2/3})^3 = (y_2)^3$ $(1+y_1^2)^2 = y_2^3$. Here,the highest order derivative is $y_2$,which represents the second derivative $\frac{d^2y}{dx^2}$. Therefore,the order of the differential equation is $2$. The degree is the power of the highest order derivative after the equation is made free from radicals and fractions. The power of $y_2$ is $3$,so the degree is $3$. The sum of the degree and order is $2 + 3 = 5$.

The sum of the degree and order of the differential equation $(1+y_1^2)^{2/3} = y_2$ is

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