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:
4 cups of water
Step-by-step explanation:
If there are 3 cups of water and 3/4 cups of sugar than there is 1/4 of a cup of sugar per cup of water so if you times that by 4 to get 1 cup of sugar you have 4 cups of water!
can you make this brainliest if its Right?
Answer:
They use Phylosophy as a means of Spiritual cleansing.
The Pythagorean theorem.
The Demand that members must live in strict secrecy and loyalty.
The appeal to certain symbols like Tetraktys etc.
They believe the soul is destined for heaven,where it will United with the Divine.
They believe that reality including music and astronomy when at their repeat level are Mathematical in nature.
Step-by-step explanation: The Pythagorean brotherhood is believed to have originated from Sounthern Italian city known as Croton. It was started by a man called Pythagoras from Samos Greece, he is a controversial phylosopher.
The Pythagorean brotherhood formulated one the most widely used Theorems in Geometry which states that THE SQUARE OF THE HYPTHEMUS OF A RIGHT ANGLED TRIANGLE IS EQUAL TO THE SQUARE OF THE OPPOSITE AND THE BASE.
