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
Anestetic [448]
3 years ago
11

Find the solution the each of the following first order linear differential equations:

Mathematics
1 answer:
Cerrena [4.2K]3 years ago
3 0

Answer:

a. y=\frac{2}{3}x^7+cx^4

b. y=2e^{7x}-ce^{5x}

c. y=e^{-2x}arctan(e^{2x})+ce^{-2x}

d. i=e^{-2t}\left(\frac{8\left(3e^{2t}\sin \left(3t\right)+2e^{2t}\cos \left(3t\right)\right)}{13}+C\right)

Step-by-step explanation:

a) xy' -4y = 2 x^6

xy'-4y=2x^6\\y'-\frac{4}{x}y=2x^5\\p(x)=\frac{-4}{x}\\Q(x)=2x^5\\\mu(x)=\int P(x)dx=\int \frac{-4}{x}dx=Ln|x|^{-4}\\y=e^{-\mu(x)}\int {e^{\mu(x)}Q(x)dx}\\y=x^4 \int {x^{-4}2x^6}dx\\y=\frac{2}{3}x^7+cx^4

 

b) y' - 5y = 4e^7x

y'-5y=4e^{7x}\\p(x)=-5\\Q(x)=4e^{7x}\\\mu(x)=\int P(x)dx=\int-5dx=-5x\\y=e^{-\mu(x)}\int {e^{\mu(x)}Q(x)dx}\\y=e^{5x}\int {e^{-5x}4e^{7x}}dx\\y=2e^{7x}-ce^{5x}

c) dy/dx + 2y = 2/(1+e^4x)

\frac{dy}{dx}+2y=\frac{2}{1+e^{4x}}\\p(x)=2\\Q(x)=\frac{2}{1+e^{4x}}\\\mu(x)=\int P(x)dx=\int 2dx=2x\\y=e^{-\mu(x)}\int {e^{\mu(x)}Q(x)dx}\\y=e^{-2x}\int {e^{2x}\frac{2}{1+e^{4x}}}dx\\y=e^{-2x}arctan(e^{2x})+ce^{-2x}

d) 1/2 di/dt + i = 4cos(3t)

\frac{1}{2}\frac{di}{dt}+i=4cos(3t)\\\frac{di}{dt}+2i=8cos(3t)\\p(t)=2\\Q(t)=8cos(3t)\\\mu(t)=\int P(t)dt=\int 2dt=2t\\i=e^{-\mu(t)}\int {e^{\mu(t)}Q(t)dt}\\i=e^{-2t}\int {e^{2t}8cos(3t}dt\\i=e^{-2t}\left(\frac{8\left(3e^{2t}\sin \left(3t\right)+2e^{2t}\cos \left(3t\right)\right)}{13}+C\right)

You might be interested in
Given that ∠2 ≅ ∠6.
insens350 [35]

Answer:

Converse of the alternate exterior angle theorem

Step-by-step explanation:

just took the test ;)

3 0
3 years ago
Read 2 more answers
Dan earns $9.50 per hour as a dishwasher. Determine the fewest number of hours he must work to earn
Oksana_A [137]

Answer:

43 hours

Step-by-step explanation:

\frac{y}{1} :\frac{408}{9.5}

y × 9.5 = 408 × 1

9.5y = 408

9.5y ÷ 9.5 = 408 ÷ 9.5

y=42\frac{18}{19}

43 hours

8 0
3 years ago
Read 2 more answers
F. -10x &gt;45<br> Solve the two step inequality
Daniel [21]

Answer:

x < -4.5

Step-by-step explanation:

<u>Step 1:  Solve for x</u>

-10x / -10 > 45 / -10

When dividing or multiplying by a negative, the sign flips.

x < -4.5

Answer:  x < -4.5

4 0
3 years ago
Cheyenne live 7/10 miles from school.a fraction in hundredths
Tems11 [23]
7/10 in hundredths is 70/100
8 0
3 years ago
Consider the matrix being multiplied by - 7.
Elis [28]

Answer:

457

Step-by-step explanation:

8 0
2 years ago
Other questions:
  • What is the leading coefficient of the polynomial?
    10·1 answer
  • I need help draw a array to represent the problem 5 x 8
    13·1 answer
  • How many solutions will this equation have?
    10·1 answer
  • 6.988.800km convert to miles
    9·2 answers
  • Which operations is the following set closed under: {2, 4, 6, ....}?
    5·2 answers
  • In Circle Q, what is m Hint: It's not 66.
    11·1 answer
  • What is the value of x if x = 64?
    15·2 answers
  • Hi can someone pls help me with this!!!
    11·1 answer
  • Tell which statement is the best estimate for the division problem 650 ÷ 8.
    14·1 answer
  • hat is the area of one base of the triangular prism? 24 square units 48 square units 160 square units 200 square units
    9·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!