what is the degree and order of
(1+y')^2=(y')^2
To determine the degree and order of a differential equation, we need to identify the highest power of the derivative and the highest power of y present in the equation.
Let's start by rewriting the given equation in standard form:
(1+y')^2 = (y')^2
Expanding both sides of the equation, we get:
1 + 2y' + (y')^2 = (y')^2
Simplifying, we have:
1 + 2y' = 0
Now, observe that this equation doesn't involve any powers of y, only the first derivative y'. Thus, there is no highest power of y in the equation.
Therefore, the degree of this differential equation is 1 (because it involves the first derivative) and the order is also 1 (because there is no power of y present).
In summary, the given differential equation has a degree of 1 and an order of 1.