Find the equilibrium (SS) solutions T(x) for the heat equation T,(t,x) = kT (t,x), 0<.x< L, with boundary conditions: (а) Т(1,0) %— 5, Т.(, L) -D0 (b) T (t,0) = 0, T(t,L)=4

Q: e y" (t) + 2y' (t) + y (t) = h (t) ; y (0) = 0, y' (0) = (t+ 1) for0 4

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Q: Find the solution of the given initial value problem. Sketch the graph of the solution and describe…

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Q: Solve y (t) + 5y (t) + 4y(t) = h(t); y(0) = 0, y (0) - 2 where h(t)%3D tfor0 s t S2 h(t) = (2t +…

A: A differential equation with the initial conditions is called an initial value problem. In this…

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A: Solution of the differential equations using Lapalce transfermation

Q: 1 6y" + y' – 2y = 0; y(1) = 2, y'(1) = %3D 6

A: First we have to solve the differential equation, 6y''+y'-2y=0 ; y(1)=0,y'(1)=-16. Given equation is…

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: find the solution yll +2y' +2y=e-t, y(0)=0, y' (0) =0 -2t e-t +cost a e-t-e-t cost b0 e-t-e-2t +cost…

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Q: y'1=4y1+8y2+2cost-16sint y'2=6y1+2y2+cost-14sint   and y1 (0)=15 and y2 (0)=13 find y1 (t) and…

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Q: Solve: x" -x+ 5 y'=t y" - 4y-2x = -2 with x(0) = y(0) = x'(0) = y'(0) = 0 Let L{x(t)} = U(s) &…

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Q: For the following autonomous ODEs, find the equilibrium solutions, then classify each solution as…

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Q: 6. An object is dropped from the top of a building 200 m high. The object encounters air resistance…

A: Solution :-

Q: Solve: x"-x+ 5 y'=t y" - 4 y-2 x' = -2 with x(0) = y(0) = x'(0) = y'(0) = 0 Let L{x(t)} = U(s) &…

A: Solution:

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A: Given: y'= y(8 - ty)

Q: = 11. Obtain the solution using Integrating Factors Found by Inspection 1. ydx+2(y-x)dy = 0 2.…

A: 1. 2. 5.****Explanation:

Q: Find the solution of the given initial value problem: y(t) y""+y' = sec(t), y(0) = 6, y'(0) = 7,…

A: Given y'''+y'=sec(t) Also given y(0)=6,  y'(0)=7,   y''(0)=-3   To Find: The solution of above…

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Q: Solve simultaneously 2' (t) – 1 = y (t) – a(t) y' (t) = z' (t) – c/(t) æ (t) + z (t) = 1- y/(t)…

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Q: 2x" + x' + 8x = +1 2 , x(0) = 1, x' (0) = 0.

A: Given differential equation, 2x''+x'+8x=t+12,x(0)=1,x'(0)=0 The objective is to solve the…

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Q: Solve an IVP:  y'' − y = g(t); y(0) = 0, y'(0) = 2, where g(t)= 1, tt

A: When t&lt;2 then the solution:   y=32et-12e-t-1 When 2&gt;t then the solution:  y=32et-32e-t-t

Q: t 1 (17) = { { + ¹ t 0 1 1 F(s)= = =+ = /201 5² = 1+t-e¹-2(t-e¹-¹)μ(t-1) = 1+t-e¹-2(t-et-¹)μ(t-1)…

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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.