EQUATION is the order of the highest derivative appearing in it.The degree of a differential equation is the degree of the highest derivative accruing in it after the equation has been expressed in a FORM free from radicals as far as the derivatives are concerned.Calculation:Given:\(\frac{{d^4y}}{{dx^4}}=2(\frac{{d^3y}}{{dx^3}}~+~\frac{{1}}{{\frac{{dy}}{{dx}}}})^\frac{{1}}{{2}}= (y)^\frac{{1}}{{2}}\)The highest order of the above differential equation = 4IF we make the above equation-free from radicals, We have to square the above equation twice and will get degree = 4