Answer:
y = 3sin2t/2 - 3cos2t/4t + C/t
Step-by-step explanation:
The differential equation y' + 1/t y = 3 cos(2t) is a first order differential equation in the form y'+p(t)y = q(t) with integrating factor I = e^∫p(t)dt
Comparing the standard form with the given differential equation.
p(t) = 1/t and q(t) = 3cos(2t)
I = e^∫1/tdt
I = e^ln(t)
I = t
The general solution for first a first order DE is expressed as;
y×I = ∫q(t)Idt + C where I is the integrating factor and C is the constant of integration.
yt = ∫t(3cos2t)dt
yt = 3∫t(cos2t)dt ...... 1
Integrating ∫t(cos2t)dt using integration by part.
Let u = t, dv = cos2tdt
du/dt = 1; du = dt
v = ∫(cos2t)dt
v = sin2t/2
∫t(cos2t)dt = t(sin2t/2) + ∫(sin2t)/2dt
= tsin2t/2 - cos2t/4 ..... 2
Substituting equation 2 into 1
yt = 3(tsin2t/2 - cos2t/4) + C
Divide through by t
y = 3sin2t/2 - 3cos2t/4t + C/t
Hence the general solution to the ODE is y = 3sin2t/2 - 3cos2t/4t + C/t
Answer:
4π
Step-by-step explanation:
-A circle subtends a total angle of 360 ° from its center.
-The length of an arc is directly proportional to the angle it subtends from the circle's center.
#The arc's length can therefore be calculated as:
Hence, the length of the arc is 4π
Answer:
x = - 3 ± √27 or if you want it in decimal form correct to nearest hundredth:
x = -8.20, 2.20.
Step-by-step explanation:
x^2 + 6x - 18 = 0
this will not factor so we use completing the square:
x^2 + 6x = (x + 3)^2 - 9 so:
(x + 3)^2 - 9 - 18 = 0
(x + 3)^2 = 27
x+ 3 = ±√27
x = - 3 ± √27
Answer:
39 degrees
Step-by-step explanation:
97+44= 141
141 - 180 = 39
Let's reorder the equation. -4x+2x-3-6. Now we can reduce like terms. -4x+2x= -2x and -3-6= -9. Put the two back together and it is simplified to -2x-9.
