Suppose you have just poured a cup of freshly brewed coffee with temperature 90 C in a room where the temperature is 20 o C. Newton's Law of Cooling states that the rate of cooling of an object is proportional to the temperature difference between the object and its surroundings. Therefore, the temperature of the coffee, T(t), satisfies the differential equation dT = k(T – Trom) dt where Trom- 20 o Cis the room temperature, and k is some constant. Suppose it is known that the coffee cools at a rate of 2 C per minute when its temperature is 70 o C. A. What is the limiting value of the temperature of the coffee? lim T(t) - B. What is the limiting value of the rate of cooling? dT lim 1 dt C. Find the constant k in the differentlial equation. D. Use Euler's method with step stze h= 3 minutes to estimate the temperature of the coffee after 15 minutes. T(15) =

Q: Figure out the order and degree of differential equation that can be formed from the equation V(1 –…

A:

Q: Match the differential equation y′ − 2y = 0 with its solution attached.

A:

Q: verify that the function y=e^-4x is a solution to the differential equation y'' + y' - 6y =0

A:

Q: e-(x²+y³)(x dx + y dy) = 0

A:

Q: Find the general solution of the ordinary differential equation. y" +xy =x

A: Given ODE is  y''+xy=x.......(1)  Here x=0 is an ordinary point of the given differential equation…

Q: ty" -y =+t y(1) = 1 y'(1) = 5

A:

Q: Find the general explicit solution to the differential equation xyy′ = x2 + 1

A: The given differential equation is xyy'=x2+1 We have to find the general explicit solution of the…

Q: If the acceleration A(t) of an object is inversely proportional to the square of its speed S(t);…

A: If the acceleration A(t) of an object is inversely proportional to the square of its speed S(t);…

Q: It is desirable to solve the differential equation dno +(a+B)No=aN and Reach the answer No(t)-Ae (a+…

A: First order linear differential equation problem......

Q: Determine whether the function is a solution of the differential equation xy' - 4y = x°e*, x > 0. y…

A:

Q: e. Cxy +C'x + 9 = 0

A: Cxy+C2x+9=0

Q: What is the solution of the differential equation ? dy = 1 + ey-x+5 dx Í. ex-y-5 = x + c ーex-y+5 =…

A:

Q: Find the linear, nonhomogeneous differential equation with constant coefficients whose solution is e…

A: First we have to find homogeneous part of the differential equation.

Q: Solve the given differential equation by variation of parameters. x²y" + xy' – y = In(x) y(x) = ,x >…

A: Given: The equation given is x2y''+xy'-y=ln(x). Assume y=xr be the solution. Differentiate the…

Q: When à = 0 the differential equation becomes X" = 0 which gives the solution X = ax + b.

A:

Q: Determine if the differential equation (3x2y + ey)dx +(x3 + xey - 2y)dy = 0 is or is not exact; if…

A: Given problem:- Determine if the differential equation (3x2 y + ey )dx +(x3 + xey - 2y)dy = 0 is or…

Q: Solve the given differential equation by separation of variables. dp = P - p² dt et+c P = _t+c X

A:

Q: Suppose y=P(t) is the number of a certain type of bacteria on a surface, and P(t) satisfies the…

A:

Q: From the differential equation dy = x2 dx, what is the equation of y in terms of x as the curve…

A:

Q: Find the particular solution to the differential equation. x²e4Y dy = (x³ + 3) dx when x = 3, y = 0

A:

Q: Given: 1+ ce y = 1- ce 1+ ce y = 1- ce is a solution to the differential equation Show that dy 1 (ỷ…

A:

Q: e value of the constant a of (x² + 4xy)dx + (ax² + 3y²)dy if the differential equation is exact, is…

A:

Q: Assume that the number of people y(t) (in million) who have heard the President announcement  to…

A: Given the differential equation :

Q: Evaluate the Particular solution of the differential equation and find y when a = O and x = 2. If…

A:

Q: solve the first order homogenous differential equation (x² + æy) dy = (æ² + y²) dæl

A: The differential equation is given as x2+xydy = x2+y2dx It can be rewritten as dydx = x2+y2x2+xy…

Q: The complementary function(C.F.) of the differential equation (D² + 6D + 18) y = is

A: Given: D2+6D+18y=x

Q: Solve the non-homogenous differential equation below dy 2y + x - 3 dx y + 2x – 3

A:

Q: If the differential equation (g(y) + y*e")dx + (4xy³ + 4xy³eV + xy*e®)dy = 0 is exact then the…

A: Given the exact differential equation; (g(y)+y4ey)dx +(4xy3+4xy3ey+xy4ey)dy=0 The standard form of…

Q: Which of the following is the solution to the differential equation = , where y(-2) = -1? dy dx (A)…

A: Given:     To determine: The solution of the given differential equation.

Q: Match the differential equation y′ − 2x = 0 with its solution as attached

A: Here given as y'-2x=0Or dydx=2xordy=2xdx

Q: Find the particular solution to the differential equation. x2e2y dy = (x3+3) dx   when x=3 and y=0

A: To find: The particular solution of the given differential equation. Given information:

Q: The population of a particular type of fish in a lake would grow logistically according to the…

A: Given -  To find -

Q: What is the long-term behaviour of the general solution to the differential equation dy = 5(1 – y)…

A:

Q: What is the order of the differential equation? dy = 2x +3 dx 1 4

A:

Q: Show that the differential equation dy / dx = y / x is inexact and that a factor of 1 / x ^ 2 can…

A: Given differential equation is, dydx=yx.

Q: For which value of a is the differential equation (y² + axy³ )dx + (Ky²x² + 2xy) dy = 0 exact

A:

Q: the differential equation dy/dx + y/x = y^2 is solved via the substitution z=y^-1, the resulting…

A:

Q: Determine if the function y= f(x) is a solution of the given differential equation .   y= 2e^-3x ,…

A: yes, the differential equation is right

Q: What is the for the exact differential equation (3ry - 5x4) dr + (y+ 3ry) dy =0 A) 9xy B) 9xy ry D)…

A: The given differential equation is 3x2y3-5x4dx+y+3x3y2dy=0. Note that 3x2y3-5x4dx+y+3x3y2dy=0 is of…

Q: In some chemical reactions, the rate at which the amount of a substance changes with time is…

A:

Q: Given y" + (y)° + 5 = 0 is a differential equation with degree 3 and order 5 O TRUE O FALSE

A: Topic = Differential equation FALSE

Q: Eliminate the arbitrary constants to find the differential equation y = C¡e¬* – C2e-2x + Cze-3x

A:

Q: If the acceleration A(t) of an object is proportional to the square root of its speed S(t); write…

A:

Q: y is related to X through the differential equation: = ax + bx² + cx³ da and y = d when X = 0 where…

A:

Q: If the acceleration A(t) of an object is proportional to the square root of its speed S(t), what is…

A:

Q: I. Find the differential equation by eliminating the arbitrary constant/s. 1. y-¹ = x(3e² + c)

A: Given That : y-1=x(3ex+c) To Find: Differential Equation by eliminating the constant

Q: If the acceleration of an object is proportional to the natural log of its speed, what is the…

A: We will use A to denote acceleration and S to denote speed of the object at any time to.

Q: Suppose y=P(t) is the number of a certain type of bacteria on a surface, and P(t) satisfies the…

A: Now,         Suppose y=P(t) is the number of a certain type of bacteria on a surface,          and…

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.