Determine whether the following ODE isexact or not ?+ =2 2 0y dx xy dy
Question
Determine whether the following ODE isexact or not ?+ =2 2 0y dx xy dy
Solution
To determine whether the given ODE is exact or not, we need to check if it satisfies the exactness condition.
The exactness condition states that if an ODE can be written in the form M(x, y)dx + N(x, y)dy = 0, then it is exact if and only if ∂M/∂y = ∂N/∂x.
In the given ODE, we have M(x, y) = x^2 and N(x, y) = xy.
Now, let's calculate the partial derivatives:
∂M/∂y = 0 ∂N/∂x = y
Since ∂M/∂y is not equal to ∂N/∂x, the given ODE is not exact.
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