Q3. An ordinary differential equation of a horizontal string which is freely pinned at both ends is given by d²y a²y dx2 P (x² – lx), where a? = EI 2EI Find the deflection of the string at any point. [10]

Q: 12. Consider the equation x = ( 1 ) x x' -5 -3 Express the general solution in terms of real valued…

A: The given system of differential equation is:x'=1-51-3 x

Q: Find the derivative of the function. e9u y = e9u + e - 36 (" +e")2(e2u – 1 +2–2u)²(6eu – 1 + 6–6«)²…

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Q: ds 4. Evaluate s = In cot 20 in terms of de

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Q: ) [3.4] A population of ants grows at a rate which is proportional to the size of the population.…

A: Please refer the attached image for complete solution.

Q: Find the third derivative of f(x) = ³/15z + 1. f"" (2) - ab a b √a |a| π sin (a) 2.

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Q: Given y - 2x2 – 4x + 9 (a) Find the differential dy. (b) When x changes from 2 to 2.05 what is the…

A: y=2x2-4x+9 Differentiating with respect to x dydx=ddx(2x2-4x+9)dydx=2*2x-4dydx=4x-4dy=(4x-4)dx

Q: Find a particular solution y, of the following equation. Primes denote the derivatives with respect…

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Q: (a) Differentiate both sides of the equation above with respect to t to get an equation that relates…

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Q: (a) Find the derivative. y In(4x – 5) – 3 In(x) dy dx (b) Find the derivative. 4x - 5 y = In x3 dy…

A: a) First we shall find the derivative of y=ln4x-5-3lnx Now,…

Q: Given f(x) = e* +x- 5, find the first and second steps in Newton's Method to approximate the zero of…

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Q: hildsmath) A 1800 L tank contains 500 L of water with a salt concentration of 20 g/L. Water with a…

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Q: 5. Solve the cubic equation by trial and error or by factoring. x³ + x² - 4x -4 = 0

A: Note: Hi! Thank you for the question As per the honour code, We’ll answer the first question since…

Q: 2. The acceleration e²t - 25 of a particle at time t > 0 is given by a(t) + 2. Given that the…

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Q: An antibiotic is administered intravenouslyinto the bloodstream at a constant rate r. As the drug…

A: Given differential equation model for antibiotic in the bloodstream is  dydt=r-ky, k>0  where k…

Q: Consider the function P = –0.5x² + 20x – 18. Find the differential for this function.

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Q: Find the differential of the function. p = 7q – 6g3/2 dp =

A: Consider the function, p=7q-6q32

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.