Answer: 6
Step-by-step explanation:
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
To simplify x^2-3 =5x
You would first subtract 5x from both sides
X^3-5x-3
Next you would plug this into the quadratic equation:
X=5+/- the square root of: -5^2 -4(1)(-3)/2(1)
Then simplify,
5+/- the squareroot of 24 + 12 / 2
5+/- The squareroot of 36 /2
5+/- 6 / 2
Then solve if it’s an addition or subtract
5+6/2
X=11/2 or 5 1/2
5-6/2
X= -1/2
The answer is x=-1/2 or x=11/2
Hope this helps
1 divided by 3
Turn fraction into decimal
Since it is repeating, and it's a 3, you don't need to round it up
The rule is 5+ = round up while 4- = round down.
