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
Leni [432]
2 years ago
8

Solve the differential equation. y' + 5xey = 0.

Mathematics
1 answer:
Gwar [14]2 years ago
8 0

Answer:

The solution is     y = - ln(\frac{5}{2}x^{2} + C)

Step-by-step explanation:

To solve the differential equation, we will find y

From the given equation, y' + 5xey = 0.

That is, y' + 5xe^{y} = 0

This can be written as

\frac{dy}{dx} + 5xe^{y} = 0

Then,

\frac{dy}{dx} = - 5xe^{y}

\frac{dy}{e^{y}}   = - 5x dx

Then, we integrate both sides

\int {\frac{dy}{e^{y}}}  =\int {- 5x dx}

\int {e^{-y}dy }}  =\int {- 5x dx}

Then,

-e^{-y} = -\frac{5}{2}x^{2} + C

e^{-y} = \frac{5}{2}x^{2} + C

Then,

ln(e^{-y}) = ln(\frac{5}{2}x^{2} + C)

Then,

-y = ln(\frac{5}{2}x^{2} + C)

Hence,

y = - ln(\frac{5}{2}x^{2} + C)

You might be interested in
John find 1/5 of the bar chocolate he bought was already eaten by his brother. He eat 3/4 of what was remaining. Find the portio
larisa86 [58]

Answer:

1/5 is left.

Step-by-step explanation:

Portion remaining after the bar was eaten by his brother = 1 - 1/5 = 4/5.

Portion remaining after John ate 3/4 of this = 4/5 - 3/4* 4/5 = 4/5 - 3/5

=  1/5.

3 0
3 years ago
Please help me with this surds question.
noname [10]

the answer is 0.2 or one fifths

3 0
3 years ago
Harold bought 20 toys for his nieces and nephews. The least expensive toy cost $6.19, and the most expensive toy cost $9.81. Whi
nikklg [1K]

Answer:

160 dollars

Step-by-step explanation:

So you would add 6.19 and 9.81 together. Then divide it by 2.  You would get 8. Then multiply it by 20 and you would get 160 dollars

8 0
3 years ago
PLEASE ANSWER <br><br> Which characteristic is shared by both prokaryotes and eukaryotes?
Norma-Jean [14]

Answer:

the 3rd one,

Step-by-step explanation:

Because it is the 3rd one

7 0
2 years ago
Read 2 more answers
HELP HELP HELP
mojhsa [17]

Answer:

2998 ; 17%

Step-by-step explanation:

Given the function:

t(c)=-3970.9(ln c)

c = % of carbon remaining ; t = time

1.) c = 47% = 47/100 = 0.47

t(0.47) = - 3970.9(In 0.47)

t = - 3970.9 * −0.755022

t = 2998.119

t = 2998

B.)

t = 7000

t(c)=-3970.9(ln c)

7000 = - 3970.9(In c)

7000 / - 3970.9 = In c

−1.762824 = In c

c = exp(−1.762824)

c = 0.1715596

c = 0.1715596 * 100%

c = 17.156% ; c = 17%

8 0
3 years ago
Read 2 more answers
Other questions:
  • Partial products 42x5
    9·2 answers
  • How to write 0.326 in two forms
    14·1 answer
  • grandma jean can make 2 blankets in 3 days if grandma jean needs to make 14 blankets how many days will it take her.
    12·1 answer
  • Car is moving on a circle on a plane. At time t (seconds), its x-coordinate is given by x(t) = 10 sin(200t + 3) + 30 while its y
    11·1 answer
  • Among all pairs of numbers whose difference is 16​, find a pair whose product is as small as possible. What is the minimum​ prod
    10·1 answer
  • Please help me ASAP! Giving brainliest
    7·1 answer
  • How do you write 9.11 x 10 4 in standard form?​
    13·1 answer
  • Find the missing length indicated.
    11·2 answers
  • Can someone help me please
    5·2 answers
  • On September 1, 2012, Ramos Inc. approved a plan to dispose of a segment of its
    5·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!