Solve the following differential equations: dy= y (log y- logx+1) (AMIETE, Summer 2004)dx18. x-Ans. log 2Cx%3Dxy log dx + y² – x² logy19.given that y (1) = 0|Ans.2y?x²-log-3+ log y = 1-4e?--yy 4y2

"Since you have asked multiple questions, we will solve the first question for you. If you want any…

Answered: dy 18. x = y (log y-log x+1) (AMIETE,…

dy 18. x = y (log y-log x+1) (AMIETE, Summer 2004) dx Ans. log2= Cx 19. xy logdx+| y -x² log dy = 0 given that y (1) = 0 y 3 + log y = 1- 4e? -log 2y2 y 4y2

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter4: Polynomial And Rational Functions

Section: Chapter Questions

Problem 5T

See similar textbooks

Related questions

Q: 2. Ifƒ (x, y) = log (x² + y²), then ƒ +ƒ is equal to XX yy 1 (a) x² + y² (b) 0 1,² - x² (c) (d) *…

Q: A population is growing according to the logistic model:- N = 5000/ 1 + e 4.8-1.9t where t is the…

A: Solution:Given N=50001+e4.8-1.9tFormula:Average poupulation over[a,b]P=1b-a∫abN(t)dt

Q: 8. In V5x 3 y z2 9. log. V xt 10. loga Va b5

Q: More models For each of the models listed below,predict y when x = 2.a) yn = 1.2 + 0.8 log x d) yn2…

A: Hey there! Thank you for posting the question. Since your question has more than 3 parts, we are…

Q: 6. More models For each of the models listed below, predict y when x = 2. a) ŷ = 1.2 + 0.8 log x d)…

Q: pmogeneous a²u ду? du a. (y + 2)² – 2x log y + k - In u = 2e¬*, k > 0 ax? ду b. и хх + ху иҳу + y?u?…

Q: Find y’ when y^2 e^2x = 3y + x^2 and y(0) = 3 a. -5 b. -7 c. -6 d. -4 e. -2 f. -1 2. Find the…

Q: Find Y and simplify whenever possible. dx 1. y = log v2x – 8 6. y = log V12x 2. y = In -1 7. y = x**…

Q: (-1. 1) (3. 1) (1. 0) y= log,) What is the equation of s)? A. log : (x+4) C. log : (x) +4 B. log :…

Q: 5. (x² + y² + x) dx − (2x² + 2y² −y)dy = 0 [Answer : x - 2y + log(x² + y²) = c]

Q: Find if z = log2 y – 6 log5 y. dy dz dz In- dy y In 10 dy y ln 10 Option 1 Option 4 64 dz In- 64 dz…

A: We know, ddxlogax = 1x·ln a a·ln b = ln ba ln a - ln b = ln ab

Q: Y Let A(x) constant, is a solution of (x³ - x) dy dx +x Then, A is = = log x + C Where C is an…

A: Given yA(x)=log x+C, where C is an arbitrary constant, is a solution of (x3-x)dydx-(3x2-1)y=x5-2x3+x…

Q: dy et y = (x³ – 18x)m(=). Find using the method of logarithmic dx - ifferentiation. Express your…

A: Topic:- derivatives

Q: Suppose that dP/dt- 0.14P(t) represents a mathematical model for the growth of a certain cell…

A: Given:the growth of a culture at time t is dPdt = 0.14P(t)P = 2 million cells

Q: log x y = dy dx 5+5ln5logx x² In5 dy 5-5ln5log x dx x² In5 Option 4 Op tion 3 dy _ 5-5ln5logx x² In5…

Q: The natural law of decay is used to study the radioactive decay of Radium: dm = -km dt Where m is…

A: This question is related to differential equations, we will solve it using given information.

Q: A large corporation starts at time t= 0 to invest part of its receipts continuously at a rate of P…

A: We have to find function

Q: A relationship between (y – 2) and (x- 1)is given by (y – 2) = a b(x-1). With a suitable lincar…

A: relationship between (y-2) and (x-1) is (y-2) = ab(x-1) So we will find the solution using logarithm…

Q: The human population x of a certain island satisfies the logistic law dx/dt = kx – Ax² with k = 0.03…

A: Given that, The human population x of a certain island satisfies the logistic law dxdt=kx-λx2 with…

Q: The natural law of decay is used to study the radioactive decay of Radium: dm -km dt Where m is the…

Q: (C) y = -log3 x (G) y = log3(1 – x) (A) y = log3 x (B) y = log3(-x) (F) y = log3(x – 1) (D) y =…

A: Find the following graph:A) y=log3xB) y=log3(-x)C) y=-log3xD) y=-log3(-x)E) y=log3x-1F)…

Q: 1. Find the value of y. a. log;25 y b. logy32 = 5 c. log,y

Q: 12. f(x) = 3* %3D 15. f(x) = %3D 18. f(x) = log3X

Q: Suppose the population of a city is modeled by the logistic equation dP dt P, 100 P(0) = 1 Use…

A: Given :

Q: dy Solve the initial-value problem for y as a function of r. (4 x) = 1, y(0) = 4 de…

A: Given initial value problem is,

Q: Suppose you want to start saving for retirement. You decide to continuously invest $15000 of your…

A: p

Q: Suppose that a population develops according to the logistic equation dP = 0.2P – 0.0005 P² dt |…

A: NOTE: Refresh your page if you can't see any equations. . factor out 0.2P

Q: Suppose the logistic curve y(t) = satisfies that y(0) = 6. What is the 1+6e-7t carrying capacity?

Q: 2. 18|ャ 2. 1. 1. 1. 1. y= 2 log2 x 1/4

Q: If T = 1o, then log T is equivalent to: 5 A (1 +2 log x) – log y B log(1 +2x) – log y (1- 2 log x) +…

A: We can find the log as below

Q: 2. Suppose that a certain population obeys the logistic equation dy (1-) ry dt k (a) If the initial…

A: Population does not exceed the carrying capacity k.

Q: Suppose that dP/dt - 0.18P(t) represents a mathematical model for the growth of a certain cell…

A: Given that dP/dt = 0.18 P(t) Where P(t) is the size of culture at time t.

Q: a. (y + 2)²0-2x log y a²u Əy² b. uxx + xy Uxy + y²u² = 0 c.t²u=√√2+x²u əx² at² + koy - Inu = 2e-x, k…

Q: HW4: 1) Find dy/dt for if: y = log2 (81ln 2) 2) Evaluate the following integra In 2 ( log2 (x + 2)'…

Q: A small manufacturing business has a group life insurance contract on it employees. Suppose that the…

A: Given, Lognormal distribution: E(S) = 0.085 V(S) = 25.32

Q: 4. The demand for Good x is Đ(p) = 1000 – p+ logM, where p is the price of Good x and M is the…

Q: Suppose that y = P(t) represents the population of a city at time t. What does represent? At ΔΡ

A: We know that

Q: If y = log x + ex then dy/dx = log x + ex a. True b. False

Q: Differentiate y = 3e +7 ln(2x) + log, x- 4" O y' = 15e5 ++ 1 - 4* In 4 %3D - I In 2 O y' = 15e5-1 1…

A: We have to differentiate y = 3e5x + 7 ln(2x) + log2x - 4x.

Q: A logistic initial value problem is given by dP — kP(М — Р), P(0) — Ро. dt M Po i. Show that P(t) Ро…

A: Part (i): First separate the logistic equation and integrate it by using the partial fraction:…

Q: 4. x (x - y) dy + y dx = 0 (U.P. B. Pharm (C.O.) 2005) Ans. y = x log Cy

A: Note: Since you have asked multiple question, we will solve the first question for you. If you want…

Q: growth model for a population of bacteria is given as P(x) = 25e 2t where t is measured in days.…

Q: The human population x of a certain island satisfies the logistic law dx/dt with k = 0.03 = 3 x…

Q: dy Which of the following could not be the graph of a particular solution to the logistic…

A: The given differential equation is dydt=0.8y(1-y20)…

Q: 25 *26. X * d Cxy') + 4y sin(2 log x), y(1) = 1, y(3) -0 dx

Q: The human population x of a certain island satisfies the logistic law dx/dt = kx – Ax² with k = 0.03…

Q: 2) d d (*) 으(1og x)- (log x)은 () (*)* d ( log x dx dx (b) dx 2

Q: A radioactive material disintegrates at a rate proportional to the amount currently present. If Q(t)…

A: dQ/dt = -rQ Hence, dQ/Q = -r.dt Integrate blindly, without any further delay to get, lnQ = -rt + c…

Q: An observation indicates that the frog population Q(t) in a small pond is 25 initially and satisfies…

A: We have to solve given differential equation to find population after t years and then find…

Concept explainers

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.

Question

Solve the following differential equations:

dy
= y (log y- logx+1) (AMIETE, Summer 2004)
dx
18. x-
Ans. log 2
Cx
%3D
xy log dx + y² – x² log
y
19.
given that y (1) = 0
|
Ans.
2y?
x²
-log-
3
+ log y = 1-
4e?
--
y
y 4y2

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Step 3

VIEW

Step by step

Solved in 3 steps

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Differential Equation$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, advanced-math and related others by exploring similar questions and additional content below.

Similar questions

The formula for the amount A in an investmentaccount with a nominal interest rate r at any timet is given by A(t)=a(e)rt, where a is the amount ofprincipal initially deposited into an account thatcompounds continuously. Prove that the percentageof interest earned to principal at any time t can becalculated with the formula I(t)=ert1.
Use the result from the previous exercise to graph the logistic model P(t)=201+4e0.5t along with its inverse on the same axis. What are the intercepts and asymptotes of each function?
What is the carrying capacity for a population modeled by the logistic equation P(t)=250,0001+499e0.45t ? initial population for the model?
The population of a culture of bacteria is modeled by the logistic equation P(t)=14,2501+29e0.62t where t is in
To the nearest whole number, what is the initial value of a population modeled by the logistic equation P(t)=1751+6.995e0.68t ? What is the carrying capacity?
Recall that the general form of a logistic equation for a population is given by P(t)=c1+aebt , such that the initial population at time t=0 is P(0)=P0. Show algebraically that cP(t)P(t)=cP0P0ebt .