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
solniwko [45]
3 years ago
5

Find the general solution of dz/dt=5ze^(sint)cost+2e^(sint)cost

Mathematics
1 answer:
gizmo_the_mogwai [7]3 years ago
4 0

Answer:

The general solution of given differential equation is \frac{1}{5}ln|5z+2|=e^{\sin t}+C.

Step-by-step explanation:

The given differential equation is

\frac{dz}{dt}=5ze^{\sin t}\cos t+2e^{\sin t}\cos t

Taking out common factors.

\frac{dz}{dt}=(5z+2)e^{\sin t}\cos t

Using variable separable method, we get

\frac{dz}{5z+2}=e^{\sin t}\cos t dt

Integrate both sides.

\int\frac{dz}{5z+2}=\int e^{\sin t}\cos t dt

I_1=I_2         .... (1)

First solve LHS,

I_1=\int\frac{dz}{5z+2}

Substitute 5z+2=u

5\frac{dz}{du}=1

dz=\frac{1}{5}du

I_1=\frac{1}{5}\int\frac{du}{u}

I_1=\frac{1}{5}ln|u|+C_1

I_1=\frac{1}{5}ln|5z+2|+C_1

Now, solve RHS,

I_2=\int e^{\sin t}\cos t dt

Substitute \sin t=v,

\cos t\frac{dt}{dv}=1

\cos tdt=dv

I_2=\int e^{v}dv

I_2=e^{v}+C_2

I_2=e^{\sin t}+C_2

Subtitle the values of I₁ and I₂ in equation (1).

\frac{1}{5}ln|5z+2|+C_1=e^{\sin t}+C_2

\frac{1}{5}ln|5z+2|=e^{\sin t}+C_2-C_1

\frac{1}{5}ln|5z+2|=e^{\sin t}+C

Therefore the general solution of given differential equation is \frac{1}{5}ln|5z+2|=e^{\sin t}+C.

You might be interested in
Please I need help. <br> Find the value of u.
seropon [69]

Answer:

62 is the answer.

Step-by-step explanation:

I hope this helps you.

8 0
2 years ago
To be a vertical angle, the angles have to be next to each other. <br> A. True<br> B. False
12345 [234]
False, vertical angles are not next to each other but opposite of each other
3 0
3 years ago
There is a child that weighs 90 pounds and every time he eats pizza he gains 5 pounds every week if he ate pizza for 3 weeks how
vladimir2022 [97]

Answer: 105

Step-by-step explanation: 90+5+5+5

7 0
3 years ago
Solve this : <br> 1. <img src="https://tex.z-dn.net/?f=6" id="TexFormula1" title="6" alt="6" align="absmiddle" class="latex-form
leonid [27]

6/2 (2+1)

6/ 2 x (3)

6/6 = 1

5 0
3 years ago
Will name you brainliest
Aleks [24]

Answer:

C po thanks

Step-by-step explanation:

sana po makatulong po sa inyo to

7 0
3 years ago
Other questions:
  • What is 19/20 as a terminating decimal?
    11·2 answers
  • The following list shows the number of video games sold per day at a video store.
    6·1 answer
  • Micah's eye-level height is 30 ft above sea level, and Mikayla's eye level height is 120 ft above sea level. How much further ca
    5·1 answer
  • A box has a length of 15 centimeters, a width of 22 centimeters, and a height of 9 centimeters. What is the surface area of the
    7·1 answer
  • These triangles are not drawn to scale. Use the Pythagorean Theorem to determine which triangle is a right triangle. Question 4
    8·2 answers
  • Brendan has $65 worth of balloons and flowers delivered to his mother. He pays the bill plus an 8.5% sales tax and an 18% tip on
    5·1 answer
  • Which of the following angles are supplementary to 7? select all that apply.
    7·1 answer
  • Pls help im confused with this
    11·1 answer
  • The values of a,b, and c in scientific notation are 3.47 x 10^-6, 4.61 x 10^-7, and 5.52 x 10^-7, respectively. Complete the fol
    10·1 answer
  • Help trigonometry<br> cccccc
    7·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!