a) y = e2t+4
When
Y = ex
dy/dx = y' = ex d(X)/dx
dy/dt = d(e2t+4)/dt
Y = e2t+4 (d(2t+4)/dt) = 2 e2t+4
b) y = t et
dy/dt = Y = et (dt/dt) + t (d(et)/dt)
Y = et + t et
C) y = t2 e2t
dy/dx = Y = t2 (d(e2t)/dt) + e2t (d(t2 )/dx)
Y = t2 2e2t + e2t 2t
d) y = log (7 t5) = log 7 + log t5t5
y = log 7 + 5 log t
dy/dx = Y = (d log7/dt) + 5 ( d (log t )/dt )
Y = 0 + 5/t
Y = 5/t
2. Find the dy/dt for each of the following: a) y = 24 b) y = te c) y=t'eat d) y = log(7) e) y = log|7t(1 - )
(1 point) A. Solve the following initial value problem: dy dt cos (t)-1 with y(6) tan(6). (Find y as a function of t.)
(1 point) A. Solve the following initial value problem: dy dt cos (t)-1 with y(6) tan(6). (Find y as a function of t.)
Find the time constant t of the following differential
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13, Find the time constant τ from the following differential equation, dt dt given that x is the input, y is the output and, a through g are constants. It is known that for a first-order instrument with differential equation a time constant r- alao dy the
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7. Assume x and y are functions of t. Evaluate dy/dt for each of the following. (a) y2 - 8x3 = -55, 5= -4,2 = 2, y = 3 (b) = 2, r = 4, y = 2 (e) cell = 2 - In 2 + In 2, 6,2 = 2, y = 0
1a) Find dy/dx x = te', y = t + sin t b) Find dy/dx and d’y/dx2 for which t is curve concave upward x = x3 + 1, y = t - c)Find the points on the curve where the tangent is horizontal or vertical. Draw the graph x = 13 – 3t, y = t3 – 312 d) Find the area enclosed by the x-axis and the curve x = t3 + 1, y = 2t – t?....
slove the system eqution: d^3y(t)/dt^3 - 2 d^2y(t)/dt^2 - 5 dy(t)/dt +6 y(t) = 2 d^2u(t)/dt^2 +du(t)/dt +u(t) A) compute the transfer function Y(s)/U(s)? B)Find inverse Laplace for y(t) and x(t)? C) find the final value of the system? D)find the initial value of the system? Please solve clearly with steps.
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#6 (50 pts) Find the general solution of the given system. = x+y dt dy dt -2x - y
Solve these differential equations: 1.) dy/dt = P[(1/y)-1] +by-a 2.) dy/dt = b*y* e^(-ct) 'P', 'b', and 'a' are constants. Thanks.
12 dạy dy 6 +9y=4e3t; when t=0, y = 2 dt dy and dt dt2 = 0