The DE dy/dt = µy – oy², µ > 0 and o > 0 occurs in the study of population dynamics. It has general solution y=

Q: Ans: (x + y)e+y = C y'+--2

A: Given differential equation is homogeneous differential equation which can be solved by converting…

Q: ty'+(1+t)y=t provide integrating factor and solution

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Q: yd the geroral solution uf y3y'+2y= 4&=2xe

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Q: + x + + 3y where x(0) = 0 and y(0) = 0. ||||

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Q: Find the particular solution of y' =(2x)/1+2y y(2)=0

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Q: Find a suitable integrating factor to solve the first the first order linear differential equation…

A: Y(X)= x2+x

Q: Solve the IVP y" + 2y' + y = U (t – 3), y(0) = 0, y'(0) = 1. -

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Q: Solve DE (1+e** )ax +e x/y 1 dy=0

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Q: Find a function F(x,y) whose level curves are solutions to the differential equation (x2 + 4xy)dx +…

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Q: Consider the function h : Z × Z → Z ×Z defined by h(x, y) = (2xy, 7x – 3y). %3D (a) Is h injective?…

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Q: Find a function y=P(t)that is a solution of y'=.02y with initial condition y=100 when t=0.

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Q: (b) Solve N +e*f + (1+x*)y = 0, %3D near x = 0, if y(0) = 1; y/(0) = 0. %3D

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Q: Example: Consider the D.E (y²+x)dx+(yx² + y)dy = 0.We separate the dependant and independent…

A: given Differential equation(xy2+x)dx+(yx2+y))dy=0rewritex(y2+1)dx=y(x2+1))dyseparating…

Q: Solve the Bernoulli equation for dy dt 5y+y¹. Use the following initial condition: y(0) = 1. y = =

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Q: Find the solution y(x) of the I.V.P y"-y = 1, y (0) = 0 and y (0) = a %3D 3Da

A: First we find complementary function then particular integral and then general solution.

Q: 2 b. y" + y' - 2y = %3D

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Q: The poaching model for Species Z is Z' = a Z (1Z) - b where the variable Z represents the population…

A: The poaching model for Species Z is given as Z' = aZ(1-Z)-b, where Z represents the population of…

Q: Does the equation e" (x + 1)dx + (ye" – xe")dy = 0 have an integrating factor u(y) depending on y…

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Q: dy Vx ev+Vx¸ x > 0 %3D X dx

A: To Find the seperable differential equation

Q: Y = C1e* + C2ex + C3e2x where y(0) -D 0, y (0) %— 1, у"(0) — 2

A: The differential equation is: y=c1e-x+c2ex+c3e2x At x =0, y = 0, so c1+c2+c3=0....(1) At x = 0,…

Q: If P(x) = -1/x then the integrating factor is a. e-* 1 b. С. -x d. e-1/x

A: Consider the linear differential equation: dydx+pxy=qx The integrating factor for above linear…

Q: 2. Consider an explosion-versus-extinction population model of the form dr =r(r-1)+a dt where a is a…

A: The given equation is dxdt=x(1-x)+a If a>0, this model reprsent stocking If a<0, this model…

Q: ==== 3y' - y + 6ety3/2 = 0, y(0) = 1/4.

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Q: Allow y(x) be the solution for the following initial value problem and then find y(e):  dy/dx =…

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Q: The normalized far-zone field pattern in free space of an antenna is given by (sin é cos²ø) E = 0 <…

A: Part(a): The given function is, E=sin32θcos2φ, 0≤θ≤π2 and 0≤φ≤2π0                      ,elsewhere…

Q: Solve the initial value dy/dx = 1/x2 + 1 - 1, y(0) = 1

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Q: 4. Find the complete solution of 2x³y' = y(y² + 3x²) %3D

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