Use boundary conditions (2) in u (x, 1) = X (t) T (1) are, u (0, t) = X (0) T (t)=0 And u (L, t) = X (L) T (1) =0 Since T (1) # 0 for all t, so only condition which holds above when X' (0) =0 and X' (L) =0.

Q: 2. Given f(x)=√x+1, g(x) = 3−*,h(x) = cosx, m(x) = log[-(x − 4)] and p(x) = ¹3 The equation in fully…

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Q: on y=1-x+y=xy given that y(0) = -3

A: Given differential equation 12y' = 1 - x + y - xy Given that y( 0 ) = -3

Q: Suppose the population of a colony of ants grows at the rate P'(t) = 1 +   5 /(√ t + 1)   If…

A: Given, P'(t) = 1 + 5t+1 when t = 120 hours  then P(t) = 250  Thenm  when t = 0 hours then P(t) = ?

Q: Use the convolution to write a formula for problem: y" + 25y = f(t), y(0) = -2, y(0) = 1. |

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Q: 13. r(t) = 3 cos³ ti + 2 sin³ tj + k 14. r(t) = 4√ti + t² √tj + ln t²k 15. r(t) = e¯¹i + 4j + 5te¹k

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Q: 4. Suppose the following functions are a general solution of: y(4) + a3y/" + azy" + a;y' + a0y = 0

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Q: In this question, we are going to estimate the value of (6/5)^1/3 without a calculator, with the…

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Q: 3. Find g if g'(x) = 8x(x® – }) and g(2) = 3. %3D %3D

A: We will find g.

Q: Find a particular solution to the following first by undertermined coficients,and then by variation…

A: Step 1: To find a particular solution to the given differential equation using the method of…

Q: 3. Find the first derivative of k(x) if k(x) = e(4x – 3)

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Q: (h) xy" + 8y' +18xy = 0, xo = 1 (i) (3 — x²)y" — 8xy' - 18y = 0, xo = 0 (j) 2y" + 8xy' + 18y = 0, xo…

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Q: ƒ(x) = ln (3-x)+²x²¹ 4

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Q: GIVE AS MUCH DETAIL AS YOU CAN

A: Step 1: Step 2: Step 3: Step 4:

Q: 8) A bacterial culture has an initial population of 10,000. If its population declines to 3000 in 8…

A: Exponential model of population is given by,     P(t) = Po * e^(kt).

Q: Suppose the functions f(x) and g(x) satisfy the following: f(2)= g(2) = g(0) = 4 3 2 = ƒ'(2) = g'(2)…

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Q: lf ƒ(3) = 5, ƒ'(3) = 2, g(3) = 4, g′(3) = −2. Let h(x) = √g(x) f(x)-2g(x)* Find h' (3). 76 O-1 C 13…

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Q: 4. Let C(x) represent the cost, R(x) the revenue, and (x) the total profit, in dollars of producing…

A: Let C(x) represent the cost, R(x) the revenue and  the total profit, in dollars of producing x units…

Q: Solve the following initial value problem: + 8y = 4t with y(1) = 4. (Find u as a function of t)

A: Consider the provided question,

Q: Suppose xe¹ - 4y = 3x + 1 + le¯¹ and y(1) = -1. Find: y (1) =

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Q: Find the general solution for y''' − y'' + y' − y = 0

A: The detailed solution is as follows below:

Q: 5. Suppose that h(x) f(x) -3x²² h'(-1) = 2, and 3f'(−1) — f(−1) = 31. Find the values of f'(-1) and…

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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.