given below. Based on the phase portrait, describe (mathematically) the basin of attraction for the critical point at (1, 1). OA y <2 and I> 0 O B) 0 < y< 2 and I > 0 OOI< 2 and y > 0 OD) y >0 and r > 0 2 and = 0

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A: Method of Separation of variables

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Q: Solve the equation for heat. azu ди with 0 0 %3D ax? at u(0,t) = u(n, t) = 0 и(х, 0) — х %3D 0 <x <…

A:

Q: E e dt Evaluale

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A: The solution is given as

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A: Given that y=y(t) be the solution to the initial value problem  To find the value of y(pi)

Q: Find the solution of y' + y = , sin(t – t)y(t)dt, y(0) = 1

A: using  laplace transform we can solve the given problem using following formulas ; Ly=YLy'=sY-y0and…

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Q: ig 5E dy at t = dt 1 If y =,u, u = secx and x = nt, then - is ion A) 83 T B) 4V3 n Cho •C) 16/3 n D)…

A:

Q: Find the two-term perturbation approximation to y" = e", y(0) = 0, (0) = 0. %3D

A: Given:                                    y"= e∈y                               y(0) = 0…

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Q: Determine the linearity and solve for the general solution to the given DE * dx ecos y – x cot y dy

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Q: Find the solution of the given initial value problem. cos t y%3D t 1 y' y(T) = 0, t >0 - t-1 y(t)

A: The given equation is; y'-y/t =cost/t-1; y(π)=0.

Q: Given the IVP dy =x² – sin y, y(0)=.5 dx Estimate y(0.4) using 4th order RK method with step size…

A:

Q: Please solve the given non homogeneous heat equation ut(x,t) = uxx(x,t) − x u(0,t) = 0 u(1,t) = 0…

A:

Q: (a) Given the initial value problem dy sin (ry) + cos (x + y) + 0, y (0) = 0, da approximate y (1),…

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Q: The solution of Laplace equation d'u = 0, where 0 < x < 3 dx? and 0 < y < 2 with boundary conditions…

A: Step:-1 Since we know for Laplace equation if step size h= k then ui, j=14ui+1, j + ui-1, j + ui,…

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A:

Q: The displacement of a structure is defined by the following equation for a damped oscillation: y=9e…

A: Displacement Of A Structure Is Defined By The Following Equation For A Damped Oscillation: y = 9e^…

Q: Solve the heat transfer equation for a metal rod in one dimension, assuming a constant cross-section…

A:

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Q: Exercises 4 I. Obtain an integrating factor for the following equations- (x – y²)dx + 2xy dy = o dr…

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A: Find the complementary solution of the given initial value problem as follows.

Q: Can you help me step by step with this problem?

A: Firstly, we set u=2t and v=(3t^2-70)^5, then we fid du/dt and dv/dt

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A:

Q: Given the IVP dy – x² – sin y, y(0)=.5 dx Estimate y(0.4) using 4th order RK method with step size…

A:

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A: The phase plane of the differential equations is as follows:

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A:

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A:

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Q: Determine the steady state temperature distribution in a rectangu- lar plate of size 20cm x 20cm by…

A: Given ∂2T∂x2+∂2T∂y2=0. The boundary conditions are depicted in the figure below,

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A: GIVEN EQUATION IS LINEAR DIFFERENTIAL EQUATION.

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Q: A rectangular steel sheet is bounded by the axis x = 0, y = 0,x = a and y = b. The temperature along…

A: rectangular steel sheet is bounded by the axis x = 0, y = 0,x a and y = b. The temperature along the…

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.