Degree of the differential equation ( d y d x )^ 1 2 =5 x+4 y is

Step-by-step solution

The given differential equation is ( dy dx )^ 1 2 = 5x + 4y . Removing the logarithm by taking the exponential of both sides, we get ( dy dx )^ 1 2 = e^ 5x+4y . Squaring both sides to eliminate the fractional exponent, we obtain dy dx = (e^ 5x+4y )^2 = e^ 10x+8y . The differential equation is now in the form f(x, y, y') = 0 , where y' = dy dx . The highest order derivative present is dy dx , which is of order 1. The power of the highest order derivative in the polynomial form is 1. Therefore, the degree of the diff