[second order differential equations] linear constant-coefficient 2nd order differential are very important in electrical and computer engineering (ece), yet recitation quiz #5 shows that many of you are still struggling with that concept. here we start with such a differential equation, first a homogeneous solution and then with a forcing function for which we know the form of the particular solution, but then we move on to a more complicated forcing function and then finally to a problem with time-varying coefficients: find the entire solution for each of the following: (a) y 00 − 4y 0 + 5y = 0, y(0) = 1, y0 (0) = 0 (b) y 00 − 4y 0 + 5y = 5t 2 , y(0) = 2, y0 (0) = 0 (fractions get a little messy) find the particular solution to the following using the variation of parameters technique: (a) y 00 − 4y 0 + 5y = e 2t csc t (b) t 2y 00 − 4ty0 + 6y = t −4 .
guess i will do q.2 first
f(x)=2x+1 n g(x)=2x^2+1,
at x=0, f(0)=1=g(0)
in general a straight line like f(x) and a parabola like g(x) will intersect at most 2 times. in this case, at x=0 n 1.
x=3, f(3)=2(3)+1=7, g(3)=2(3)^2+1=19
f(x)< > g(x) at x=3
its 42 degrees
its a proportionate line so it has the same angle on both sides.