Solve the following differential equations.
i) y'''-6y''+10y'=0
ii) dy/dx= x2/(1+y2) with y(1)=3
iii) (x2-2y)y'+2x+2xy=0
iv) Use substitution to solve t2y'+2ty=y5
for t>0
Initial value problem : Differential equations:
dx/dt = x + 2y
dy/dt = 2x + y
Initial conditions:
x(0) = 0
y(0) = 2
a) Find the solution to this initial value problem
(yes, I know, the text says that the solutions are
x(t)= e^3t - e^-t and y(x) = e^3t + e^-t
and but I want you to derive these solutions yourself using one
of the methods we studied in chapter 4) Work this part out on paper
to...