Consider and solve the initial value problem of a new form of life discovered on a distant planet. Outside its habitable zone, the rate of change of population of the life form is governed by the following data: dy :+ y = f(x),where f(x) = {e-2 0 2

Q: Find the particular solution for initial value problem.

A: x2dydx-yx=0⇒x2dydx=yx⇒dyy=xx2 dx⇒dyy=x12·x-2 dx⇒dyy=x-32 dx Now integrating on both sides, we get…

Q: Solve the initial value problem e*dx + (e*tany + 2secy)dy = 0, y(1) = 2

A: Given that exdx+extaby+2sec ydy=0, y(1)=2. This is of the form Mdx+Ndy=0. M=exMy=0 And…

Q: Solve the follow ing initial value problem: 3x(t2- 1)dt+ (t³ + 8x- 3t)dx= 0, t(0)= 1

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Q: Suppose that the DE dy y(70 - y) – 600 dt models a logistic equation with harvesting, where y (t)…

A: “Since you have posted a question with multiple sub-parts, we will solve first three sub-parts for…

Q: Solve the initial value problem dy/dx= e^x+4x-3 where y=5 when x=0

A: Given dydx=ex+4x-3and when x = 0 then y = 5

Q: A tank contains 50-liters of brine in which 20 grams of salt is dissolved. Pure water is being…

A: Given: Let the rate of pumping in, Rin = 5 L / min Let the rate of pumping out, Rout = 4 L / min

Q: Solve the initial value problem dy/dx=x^2+1/x^2, y=-1 when x=1.

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Q: Solve the initial value problem. dy 3 dx - = x˚ (y - 5), y(0) = 9

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Q: In "Bats Feast," Cecilion unleashes Blood Demon power, increasing his Movement Speed and gaining…

A: This is the question of differential equations.

Q: Find the explicit solution of the initial value problem, X +y = x² ln(x) y² where y(1) = 2 and x >…

A: The equation of the form dydx+P(x)y=Q(x)yn is Bernoulli's equation. The equation is converted into…

Q: Solve the initial value problem dy/dx=2/x+1, y(0)=2.

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Q: Suppose that a quantity y = y(t) increases at a rate that is proportional to the square of the…

A: Given that a quantity y=y(t) increases at a rate that is proportional to the square of the amount…

Q: Suppose that glucose enters the bloodstream at the constant rate of r grams per minute while it is…

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Q: Solve the initial value problem for y as a function of x. x2 - 16 dy = X, x > 4, y(8) = 0 dx

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Q: Solve the initial value problem dy + X, x > 0; y(2) = 0 x3 dx

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Q: Find the logistic differential equation dy ky 1-Y dx L

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Q: Solve the initial value problem to find f(x), given 2 =1+ 4x? when f(-1) = 4 dx

A: Satisfied condition of differential equation

Q: Solve the initial value problems for x as a functionof t. (t + 1) dx/dt = x2 + 1 (t > -1), x(0) =…

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Q: dy/dx= 2ex-e-x y(0)=5

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Q: Find the logistic differential equation of dy/dx=ky(1-y/L)

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Q: Find the function which solves the initial value problem dy/dx=2x−2, y(2)=−7 y(x)=?

A: The solution is:

Q: Solve the initial value problem dy/dx=2x−1x2, x≠0, y(1)=5.

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Q: 1. The position of a particle at time t (s) is s(t) = V12 +1 m. Com- pute its average velocity over…

A: Given, The position of a particle at time t seconds is s(t)=t2+1 meter.  To find the average…

Q: A tank initially contains 400 gal of fresh water. At time t= 0, a brine solution with a…

A: As per Bartleby answering guidelines if a questions has multiple subparts then an expert is expected…

Q: Solve the initial-value problem. dy for x20 with y(0) = 2 5 dx The solution to the initial-value…

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Q: Suppose that the DE dy = y(70 – y) – 600 dt - models a logistic equation with harvesting, where y…

A: The given model of logistic equation with harvesting is, where, y(t) represents the tilapia…

Q: (x² + 4) dy 山 3. y(2) = 0

A: we know that ∫dxx2+a2=1atan-1xa+C,  where a>0 see below the answer and calculation

Q: Verify that y(t) = ceat solves the differential equation for unlimited growth, y' = ay, with initial…

A: Given Differential Equation : y1 = ay , y(0) = C i.e. dydt =ayie  dyy = adt Integratinh both side we…

Q: (b) Find an explicit solution to the initial value problem given by (y – 1) dx + x² dy = 0, y(1) = 0…

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Q: Solve the initial value problem dy/dx= 1+x+x^2/2, with y=1 when x=0.

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Q: Use a technique of integration or a substitution to find an explicit solution of the given…

A: To find the solution of the differential equation we use the method of separation of variables. We…

Q: Find an explicit solution of the given initial-value problem. () - 1 dx 3(x2 + 1), dt X =

A: Given query is to find the solution of the differential equation.

Q: dx 10x – x2, dt x(0) = 1 -

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Q: Solve the initial-value problem. (dy)/(dx) = (5)/√(x), for x ≥ 1 with y(4) = 4 The solution to the…

A: we have the differential equation  dydx=5x with y(4) = 4 having the initial value problem

Q: Solve the initial value problem: dy x(1+ y)²; y(0) = –3 dx

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Q: Solve the initial value problem dy/dx=x2−1, y(3)=7.

A: Given:

Q: The size of a population x as a function of time y is given by dx/dy=0.02x+9y . Solve for x as a…

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Q: Solve the initial value problems for x as a functionof t. (t2 + 2t) dx/dt = 2x + 2 (t, x > 0),…

A: t2+2tdxdt=2x+2⇒dx2x+2=dtt2+2t Now integrating on both sides, we get…

Q: Find the function which solves the initial value problem dy/dx= 3ex −2x;  y(0)=−1.

A: Given that dy/dx = 3ex-2x;   y(0) = 1.dy = (3ex-2x)dx            (By cross multiplying)Integrate on…

Q: dx 10х — х2, x(0) dt

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Q: A tank contains 50-liters of brine in which 20 grams of salt is dissolved. Pure water is being…

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Q: The solution of dy=(6+2y)dx subject to the initial condition y=0 when x=0 is

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Q: The special sclution to the differential equation 3 xy" + xy" – xy' +y = log(x)

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Q: solve the initial value problem dx/dt=x-x^{3} with x(0)=1 Please provide valid answer

A: Given differential equation is

Q: Solve the initial value problem. ds dt I cost- sint, s = 3 2

A: To solve the initial value problem.

Q: solve the bernoulli equation dx +1x' + = 0 +tx dt

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Q: Solve the Initial value problem:   dy/dx= ((2y)/x) - 1 , y(1)=3

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Q: Show that solving the logistic differential equation results in the logistic growth function

A: The given differential equation is dydt=825y54-y   with  y0=1. Solve the above differential equation…

Q: Solve the initial-value problem for y as a function of x. (x^2+36)dy/dx=1,y(6)=0

A:

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.