The poaching model for Species Y is Y' = 0.001 Y (1- Y)-0.001231 where the variable Y represents the population of %3D Species Y and Yo method with At = 0.5, to approximate the population = 429 when t= 0. Use Euler's %3D %3D of Species Y (to the nearest integer) when t = 4. %3D

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Q: Euler method to compute ys for the DE 2xy'=y for y(1)=1

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Q: y" – 2y' + y = -3 – x + x², y(0) = –2, y'(0) = 1. %3D %3D

A: Given: y''-2y'+y=-3-x+x2 ; y0=-2, y'0=1 So, We can also write as; D2-2D+1y=-3-x+x2   The auxiliary…

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Q: Please solve using 2nd Order and 4th Order Runga-Kutta y'=ysin^3(t)       y(0)=1 t= 0 to 3   h=0.1

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Q: (4x + 1)2 x2 - 5 Find S' if s = s' =

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Q: Exact Differe ntial Equation: x(3xy – 4y +6 kdx + (x² – 6x²y² -1\ty=0

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Q: 8²% Classify the partial differential equation: 6- dx² -16 <0, Hyperbolic -24 < 0, Elliptic O 240,…

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Q: Use Euler method to approximate the value of y(0.1), given               y' - x2 - y = 5 ,  y(0) =…

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Q: A particular solution of x²y'- x(x + 2)y' + (x + 2)y=2x³, x>0, y₁(x)=x, V₂(x) = xex

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Q: 1.y" + у %3D Зе2x

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Q: ++x* +3x +4x-x-2 Fx + G В Dx +E Given: + -+ %3D x +1 (x +1)* 3 x'(x+1) Find A ,B, C, D ,E, F, and G

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Q: y' = (1-x²)y , y(1) = 1, h = 0.1 1.0921 1.0986 1.0974 O 1.0935

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Q: 5) Use improved Euler method to find y(2) if y(1)=2 for dy xy!/3 %3D dx take h=0.5

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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.