The order and degree of the differential equation dy d x -4 dy d x -7 x=0 is respectively

Step-by-step solution

The order of the differential equation is determined by the highest derivative present, which is the first derivative dy dx in this case. To determine the degree, the equation must first be rationalized. We isolate the radical: dy dx = 4 dy dx + 7x , and square both sides, yielding dy dx = (4 dy dx )^2 + 2 (4 dy dx )(7x) + (7x)^2 = 16 ( dy dx )^2 + 56x dy dx + 49x^2 . The highest power of dy dx in the resulting expression is 2, so the degree is 2. The order is 1 and the degree is 2. The correct option is A .