10 1 y = 5 dt y(0) = -1 = 2 ot

Q: 11. (1– e'y) dt +- dy = 0, y(1) = 1

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Q: Determine the quadrants in which the solution of the differential equation dy/dx = (1/2)xy is an…

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Q: How could the 1D heat equation represent physically?

A: We know that the heat energy of a body with uniform property is represented as; where c is the…

Q: Solve the IVP -8 0] *-[× -16 dx dt x(t) = x, x(0) [8]

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Q: 16. Suppose the radius r, height h, and volume V of a dh related to dt dV cylinder are functions of…

A: Given: A cylinder with radius, r and height, h. The formula for the volume (V) of the cylinder is…

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

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Q: 12 Solve the equation. d²x dx + 4 + 3x = e-3t dt2 dt dx given that att= 0; x =} and = -2. dt

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Q: xdy +(y– xy+2)dx = 0

A: The given differential equation is; xdx+(y-xy+2)dy=0

Q: plve the initial value problem given by y" + y = (x – 1)*, y(0) = 0, y'(0) = 0

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Q: Write down a differential equation of the form =ay + b whose dy dt solutions all approach y = 6 as…

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Q: A population of insects grows at a rate that is given by dN = 0.078N dt - If there are initially 100…

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Q: 5. Find the differential equation of the family of straight lines with slope 1. с. у -130 d. y' +1=0…

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Q: dy 2. When does the differential equation Cekt represent exponential growth? exponential dt decay?

A: We need to explain growth and decay.

Q: The solution of the differential equation (logistic growth model) dy/dt = 0.2y(50 - y) is y = /(1 +…

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Q: 1 1 LGt-5- At²est + Ceisinh Dt = [(s – 1)3 ' s² + 2s – 5]

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

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Q: Find the differential equation of dy/dx = x+y/x-y

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Q: Solve the following IVP: dy dt? dy 6. + 9y = e dt 3t

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Q: The differential equation dy/dx = y(y+6) has initial condition of y(0) = 3 What is y(1)? Multiple…

A: Given

Q: Discretize the differential equation y"+y' +4ty= {t – )), y'(0) = 2, y'(3) = -2 with step-size h =

A: The differential equation given is as follows y''+y'+4ty=δt-32, y'0=2, y'3=-2 The central difference…

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

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Q: Can i get help step by step?

A: To determine the solution of the initial value differential equation.

Q: Solve the initial value problem dz/dt=cost−2sint, z(0)=5.

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Q: Verify that the function y = Ce5x is a solution of the differential equation           y′ = 5y

A: The given function is  y = Ce5x  The differential equation is y′ = 5y

Q: b) Solve the differential equation y(1-ysin(x))dx + (2x+3ycos(x))dy=0.

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Q: 1 dy Solve the initial value problem of - 2 dx y +1 cos x , y(n) = 0

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Q: Find the logistic equation that passes through the given point. dy = 1.72y 1 dt (0, 4) - 6 y =

A: We solve the given differential eqn. By method of separable variable

Q: d 6. Q. - Vi ln(t)dt equals dx a.36x° (ln x) – /2 ln(2) b. Vr6 In(x°) – V36 In(3º) с. 6а2 (In x)…

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Q: Solve the partial differential equation xp+yq=z.

A: According to the lagrange linear equation, Pp+Qq=R the solution is,

Q: dy ycosy dt ||

A: Firstly we draw the graph then draw a phase line.

Q: dp apš – Bp dt p(0) = 0

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Q: Find the differential equation 3(x2 + y2)dx + x(x2 + 3y2 + 6y)dy = 0

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Q: The differential equation for cooling of a cup of coffee is given by dT dt = -(T – Tenu)/T where T…

A: final answer is  T = 200 C at t =5 minutes detailed solution with explanation is given below

Q: Consider the differential equation 2²y" – x(x + 2)y + (x + 2)y = 0, x > 0 - 3.

A: Given: x2y''-xx+2y'+x+2y=0, x>0   To find: A second solution y2x using the solution y1x To show:…

Q: -2 2 dx dt -12 8 with the initial value -2 x(0) = -5 x(t) =

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Q: Q4: Find the general solution of the differential equation y'+ (tan x)y = sec2 x %3D

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Q: Find the general solution for each differential equation.

A: Given differential equation is: x (dy/dx) + y = 2x^2 xdy + ydx = (2x^2)dx d(xy) = (2x^2)dx The above…

Q: Solve the differential equation. dz + 5et + z = 0 dt

A: We are entitled to solve only one question at a time so, I am providing you an answer of the same.…

Q: -18 21 dx dt -14 17 with the initial value 10 æ(0) =

A: Given that ; dxdt=-1821-1417x with the initial value. x0=105

Q: dx 10х — х2, x(0) dt

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Q: The amount u of a radioactive material change in time given as a differential equation du dt = -7u…

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Q: cln 4 cln 3 cln 2 10. Compute e0.5x+y-z dz dy dx.

A: Evaluate the integral: ∫0ln4∫0ln 3∫0ln 2e0.5x+y-zdzdydx=∫0ln4∫0ln 3ey+0.5x∫0ln2e-zdzdydx=∫0ln4∫0ln…

Q: Find the differential equation of y(x-6y) dx-x(2x-9)y dy=0

A: Solution is given below:

Q: Determine order and degree of the differential equation (y")' +(y")' +(y')* + y° =0

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

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Q: The order and degree of the differential equation 14()(음) + 12음()y= 16 dy dx - dz5 dx are

A: The given differential equation is:

Q: dy - r (11 - 2) : v(0) = ; k (11–);y (0) dt 9

A: dy/dt = ry (11-y/k) integration (1/y(11-y/k)dy) = integration (rdt) R.H.S. integration (rdt) = rt+C…

Q: Find a linearization of the differential equation: d^2x/dt^2 + xe^(0.01x) = 0

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Q: Use a computer algebra system to (a) graph the slope field for the differential equation and (b)…

A: Given: dydx=4-y