Solve for G.S. / P.S. for the following differential equations using separation of variables. 2 sin^2 2t dx=cos x(1+cos 2x)dt

DofotheroU 2021-09-08 Answered
Solve for G.S. / P.S. for the following differential equations using separation of variables.
2sin22tdx=cosx(1+cos2x)dt
You can still ask an expert for help

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

Solve your problem for the price of one coffee

  • Available 24/7
  • Math expert for every subject
  • Pay only if we can solve it
Ask Question

Expert Answer

yagombyeR
Answered 2021-09-09 Author has 92 answers
Step 1
the given differential equation is:
2sin22tdx=cosx(1+cos2x)dt
we have to find the general solution of the given differential equation by using separation of variables.
separate the variables:
2sin22tdx=cosx(1+cos2x)dt
dxcosx(1+cos2x)=dt2sin22t
now integrate the both sides of the equation.
Therefore,
dxcosx(1+cos2x)=dt2sin22t(1)
Step 2
let the integral dxcosx(1+cos2x)
therefore,
I=dxcosx(1+cos2x)
now as we know that 1+cos2x=2cos2x
therefore,
I=dxcosx(2cos2x)
=12dxcos3x
=12sec3xdx
step 3
now let sec3xdx  be  I1
therefore,
I1=sec3xdx
=sec2xsecxdx
now let sec2x be the second function and the secx be the first function and solve the integral I1 by using integration by parts. therefore,
I1=sec2xsecxdx
I1=secxsec2xdx(ddx(secx)sec2xdx)dx

We have step-by-step solutions for your answer!

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

You might be interested in

asked 2021-02-05
Use polar coordinates to find the limit. [Hint: Let x=rcosandy=rsin , and note that (x, y) (0, 0) implies r 0.] lim(x,y)(0,0)x2y2x2+y2
asked 2021-09-08
Lynbrook West , an apartment complex , has 100 two-bedroom units. The montly profit (in dollars) realized from renting out x apartments is given by the following function.
P(x)=12x2+2136x41000
To maximize the monthly rental profit , how many units should be rented out?
What is the maximum monthly profit realizable?
asked 2021-11-16
a) A low voltage transformer manufacturing line has a purchase order of 1700 piece, If the manufacturing line production rate is 22 piece per minute use dimensional analysis techniques to determine the time taken to produce the requested transformers tothe nearest minut in hours and minutes.
b) Assume that the production time of a transformer can be given by the following formals:
t=Gm13v3l2
Where m is the mass of the transformer in kg, v is the velocity of the manufacturing line in ms and l is the length of the production line in meters. Find the diamensions of G.
c) In b, if m=220 grams, l=10.2m, v=2.3ms and time is 30.1 ms. Find G?
asked 2021-10-04
For a marketing analysis,you want to ask 125 people how they
like the colours red,green and blue.After your questions,your
questions,you discover that.
55 people like red.
60 people like blue.
50 people like green.
asked 2021-11-17
At HD Sport and Fitness gym, analysis shows that, as the demand of the gym, the number of members is 86 when annual membership fee is $25 per member and the number of members is 84 when annual membership fee is $33 per member. As the operator of the gym, you found out that number of members (q) and membership fee (p) have a linear relationship.
A) At what membership price, p , is the revenue maximized?
p=
Round your answer to 2 decimal places.
B) What is the maximum annual revenue?
R=.
Round your answer to 2 decimal places.
asked 2021-01-31
Nonexistence of a limit Investiage the limit lim(x,y)(0,0)(x+y)2x2+y2
asked 2021-09-11
Solve each equation over the set of complex numbers, find the magnitudes of the solutions and draw them in the complex plane. Hint: For some of the equations , to get n roots you must use a3+b3=(a+b)(a2ab+b2) and a3b3=(ab)(a2+ab+b2)
x61=0

New questions