Respuesta :
Statements is TRUE
Based on the graph of the general solution to the differential equation dy over dx equals 2 times x - 2 times y = dy/dx=2x-2y.
What is general solution to the differential equation?
A differential equation's solution is an expression for the dependent variable in terms of one or more independent variables that satisfy the relationship.
The statement which is true is the slopes are all positive in quadrant I.
Given the differential equation is dy/dx=2x-2y
A differential equation is an equation that contains at least one derivative of an unknown function, either a normal differential equation or a partial differential equation.
Given dy/dx=2x-2y
now slope=2x-2y
Along x-axis, y=0. So, slope=2x+0.
Since it depends upon x hence the slope along the y-axis are not horizontal.
Along y-axis, x=0. So, slope -2y+0.
The slope along the x-axis are also not horizontal.
In quadrant I:
x,y≥20
So, dy/dx ≥20
Therefore, the slopes are all positive in quadrant I. In quadrant IV,
x≥0,y≤0
so, dy/dx is not always positive.
The slope are not all positive in quadrant IV:
Therefore, the slope are all positive in quadrant I for the differential equation dy/dx=2x-2y.
General solution to the differential equation =
dy/dx=2x-2y.
Learn more about general solution here:
https://brainly.com/question/14620493
#SPJ4
Complete Question:
Based on the graph of the general solution to the differential equation dy over dx equals 2 times x plus y comma which of the following statements is true?
The slopes along the y-axis are horizontal.
The slopes along the x-axis are horizontal.
The slopes are all positive in Quadrant 1.
The slopes are all positive in Quadrant 4.
