- #1
sozo91
- 5
- 0
How do I find the oblique trajectories to the following family of curves:
y = x-1 + c*e^-x
y = x-1 + c*e^-x
To find oblique trajectories to y=x-1+c*e^-x, you can use the method of undetermined coefficients. This involves assuming a general solution in the form of y=Ax+B+c*e^-x and then substituting it into the original equation to solve for the coefficients A and B.
The constant c represents the initial condition or starting point of the trajectory. It determines the position of the trajectory in relation to the original curve y=x-1. Different values of c will result in different oblique trajectories.
No, oblique trajectories cannot intersect. They are parallel to each other and never cross paths. This is because they are determined by the same initial condition c, and therefore have the same slope at every point.
To graph oblique trajectories, you can plot points by choosing different values of c and solving for the corresponding y-values. You can also use a graphing calculator or software to plot the trajectories. It is important to label the trajectories with their corresponding values of c.
No, oblique trajectories are not always present in a function. They only appear when the function has a term in the form of c*e^-x, where c is a constant. If this term is not present, then there will be no oblique trajectories.