1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Eduardwww [97]
3 years ago
5

Find the solution of the differential equation that satisfies the given initial condition. (du)/(dt) = (2t + sec^2 t)/(2u), u(0)

= -1
Mathematics
1 answer:
Delicious77 [7]3 years ago
3 0
Ah okay so in differential equations you usually want the top variable isolated. To do this, multiply by dt and 2u and you get
2udu = 2t + { \sec(t) }^{2} dt
Now just integrate both sides. The integral of 2u with respect to u is u². The integral of (2t + sec²(t) with respect to t is t² + ∫sec²(t)dt. The last part is just tan(x) because d/dt(tan(t)) is sec²(t) so just integrating gets us back. Now we have
{u}^{2}   + c =  {t}^{2}  +  \tan(t)  + k
Where c and k are arbitrary constants. Subtracting c from k and you get
{u}^{2}  =  {t}^{2}  +  \tan(t)  + b
Where b is another constant. To find b, just plug in u(0) = -1 where u is -1 and t is 0. This becomes
1 =  \tan(0)  + b
tan(0) is 0 so b = 1. Take the plus or minus square root on both sides and you finally get
u =  \: { {t}^{2} }  +  \tan(t)  + 1
But Brainly didn't let me do but juat remember there is a plus or minus square root on the left.
You might be interested in
Which best represents the solution for the inequality-100 > -5y
Ira Lisetskai [31]
Y > 20

Hope this helps! Message back for an explanation:)
8 0
3 years ago
gale's grade in science for the term is determined by the average of five test grades. his first four grades are 80, 95, 78, and
lara [203]

Answer:

He needs at least 77 on the 5th test.

<em>T₅ ≥ 77</em>

Step-by-step explanation:

If five numbers are to average 84, then their sum must be (5 x 84) = 420 .

Gale needs his five grades to add up to 420.

So far, he has (80 + 95 + 78 + 90) =  343 .

He needs at least (420 - 343) = <em>77 more</em> points on the 5th test.

5 0
3 years ago
Helpp please will mark brainlest
hram777 [196]

Answer:

what do you need help with?

Step-by-step explanation:

8 0
2 years ago
Read 2 more answers
Add 408 to the difference of 7 000 and 3 096​
egoroff_w [7]

Answer:

4312

Step-by-step explanation:

7000-3096=3904

3904+408=4312

7 0
2 years ago
Okay so we have this question of the week thing and this week our answer is 8 so i need a algebra problem that is a two step equ
Inessa05 [86]

Answer:

2x+4=8

x=2

2 times 2 equals 4

Four plus four is 8

5 0
3 years ago
Other questions:
  • 5(x+y) use the distributive property
    6·2 answers
  • Dylan has two cubes of iron. The larger cube has twice the mass of the smaller cube. He measures the smaller cube. It's mass is
    6·1 answer
  • ILL MARK YOU AS BRAINLIEST, RATE YOU A 5, AND THANK YOU! 70 POINTS!
    7·2 answers
  • Cindy has a poster in the shape of a parallelogram. What is the area of this parallelogram? 2.85 ft² 3.60 ft² 4.35 ft² 15.21 ft²
    14·1 answer
  • the number is service upgrade sold by each of 30 employees is as follows :32,621,10,8,11,12,36,17,16,15,18,40,24,21,23,24,24,29,
    9·1 answer
  • The prices of karaoke at 6 different stores are $77, $85, $78, $72, $80 and $118. What is the outlier in tbe data set?
    6·1 answer
  • Please help!!!!!!!!!!!!
    6·1 answer
  • Anyone good with calculus? Please help.
    5·1 answer
  • Plz help im stuck!!!!!!
    5·1 answer
  • What single percentage change is equivalent to a 23% decrease followed by a 16% increase?
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!