Final answer:
To determine the value of b for which the given differential equation is exact, we need to check if the equation satisfies the condition ∂M/∂y = ∂N/∂x. If the equation satisfies this condition, it is exact. The value of b for which the given differential equation is exact is the same as the coefficient of dx in the equation.
Step-by-step explanation:
To determine the value of b for which the given differential equation is exact, we need to check if the equation satisfies the condition:
∂M/∂y = ∂N/∂x
If the equation satisfies this condition, it is exact.
We can consider the given differential equation as:
M(x, y) + N(x, y) * dy/dx = 0
Comparing coefficients, we have:
M(x, y) = ax + by + c
N(x, y) = dx + ey + f
Now, we find the partial derivatives:
∂M/∂y = b
∂N/∂x = d
For the equation to be exact, b should be equal to d. Therefore, the value of b for which the given differential equation is exact is the same as the coefficient of dx in the equation.