Solving the following odes: (a) y" - 2y' - 3y = e^-x: (b) y'" + 3y" + 3y' + y = e^-x (x - 5);

Key features: the functions can not be parallels, this means that their respective slopes can not be equal or multiple to the other

Step-by-step explanation:

Take for instance 2 linear functions,  and

If they intersect in some point in the space, say that is

Then (x1,y1)=(x3,y3), (x2.y2)= (x3,y3)

So, we can compare the two functions and get the following result;

It tells us that if M=m, we get an error, meaning that the functions are in fact parallels and there is no way that they meet in some point.

hope this helps!