Let c be a positive number. a differential equation of the form
dy dt= ky1 + c where k is a positive constant, is called a doomsday equation because the exponent in the expression ky1 + c is larger than the exponent 1 for natural growth.
(a) determine the solution that satisfies the initial condition
y(0) = y0.
ans: y=(-ckt+y0^-c)^(-1/c)
(b) show that there is a finite time t = t (doomsday) such that lim t %u2192 t%u2212y(t) = infinity. ans: y(t) --> infinity as 1-cy0^ckt--> 0 as t--> 1/cy0^ck t=1/cy0^ck, them lim y(t)=infinity as t--> t-
The linear combination method is applied to a system of equations as shown. 4(.25x + .5y = 3.75) → x + 2y = 15 (4x – 8y = 12) → x – 2y = 3 2x = 18 what is the solution of the system of equations? (1,2) (3,9) (5,5) (9,3)
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