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
9. In a school, there are 120 students in a particular year group. Out of those students, 100 study
Tresset [83]
This does not make any sense I don’t know how to help you out sorry
6 0
2 years ago
You deposit $1500 in an account that pays 7% annual interest. Find the balance after 2 years when the interest is compounded dai
just olya [345]

A = $ 1,721.28

A = P + I where

P (principal) = $ 1,500.00

I (interest) = $ 221.28

3 0
3 years ago
Find the coordinates of the vertices of the figure after the given transformation: T<0,7>
zaharov [31]

Answer: B

Step-by-step explanation:

Why did historians choose to study this topic?

7 0
2 years ago
Find the size of and an angle which is five times its supplement.
Rzqust [24]
A Pentagon 



i hoped this helped :)
6 0
3 years ago
How many different ways can you arrange 100 numbers?
Semenov [28]
10,000 or 100,000 so I hope it helps
4 0
3 years ago
Other questions:
  • Can someone please help me?
    11·1 answer
  • Use the zero-product property to solve each question.<br> 1) (2x-7)(4x+10)=0
    8·1 answer
  • Find the slope of the parametric curve xequalsnegative 4 t cubed plus 8​, yequals5 t squared​, for negative infinity less than t
    8·1 answer
  • The car owned by a person is part of his or her ____.
    15·2 answers
  • Colby and jaquan are growing bacteria in an experiment in a laboratory. Colby starts with 50 bacteria in his culture and the num
    6·1 answer
  • Easy Question<br><br> Topic: Volume<br><br> Focus on question 10
    10·2 answers
  • 14/35 as a equivalent fraction
    12·1 answer
  • John paid $50 for renting a cycle for 5 hours. Which graph shows the relationship between the cost of renting a cycle for differ
    11·2 answers
  • The triangles shown below must be congruent.<br> O True<br> O False
    7·2 answers
  • Expressions that are equal to 4 times the square root of 5
    9·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!