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Find the length of the curve r(t) =< 3cost, 3sint, 4t > for 1 st 57.
Find a general solution to the given equation for t<0. y''(t) – Ły'(t) + 5 -y(t) = 0 t The general solution is y(t) = (Use parentheses to clearly denote the argument of each function.)
6 3. Consider x = [<1 %)* 3. Consider x' = | (a) Find the general solution to the system and describe the behavior of the solution as t + +00 (b) Draw a direction field and plot a few trajectories of the system.
Find a general solution to the given Cauchy-Euler equation for t> 0. 12d²y dy + 2t- dt - 6y = 0 dt² The general solution is y(t) =
QUESTION 11 Find the solution of x' + 2x' +x=f(t), x(0)=1, x'(o=0, where f(t) = 1 if t< 2; and f(t) = 0 if t> 2.
Question 11 1p Determine the length of the curve r(t) = (2, 3 sin(2t), 3 cos(2t)) on the interval ( <t<27 47107 Озубл 47 0 250 √107 None of the above or below Previous Ne
Find the Laplace Transform of f(t)=0 if t<1: f(t) = t if 13t<2; f(t) = 0 ift> 2.
Laplace transform 0 <t<1 3. y' -5y = 10 t21 y(0)=1
5. Find the solution u(r,t) of <1.o, whic conditions u(o,t)2, u(1,t3, and the initial comdition down the complete solution u(,t)
Find the Peano range of the Cauchy problem. Z=38 {r' = (2 = (Z -t)y,-3<t< 3; y(1) = 2