dy/dx=4x/y..verify that the straight lines y=2x are solution curves, provided x doesnt equal 0.
To verify that the straight lines y = 2x are solution curves for the given differential equation dy/dx = 4x/y, we need to substitute this line into the differential equation and check if it satisfies the equation.
The given differential equation is dy/dx = 4x/y.
Let's substitute y = 2x into the differential equation:
dy/dx = 4x/y
dy/dx = 4x/(2x)
dy/dx = 2
Since dy/dx = 2, we have the following equation:
2 = 2
The equation is true, which means that the equation is satisfied.
Therefore, we can conclude that the straight lines y = 2x are solution curves for the given differential equation, given that x ≠ 0.
To verify that the straight lines y = 2x are solution curves for the differential equation dy/dx = 4x/y, we need to substitute y = 2x into the differential equation and check if it holds true.
Given: dy/dx = 4x/y
Substituting y = 2x:
dy/dx = 4x/(2x)
= 2
Now, let's calculate the derivative of y = 2x with respect to x:
dy/dx = 2
Comparing the two equations, we can see that dy/dx is equal to 2 for both y = 2x and given the differential equation dy/dx = 4x/y, when y = 2x. Therefore, we can conclude that the straight lines y = 2x are indeed solution curves for the given differential equation.