Math

Differential equations Solutions

Consider the autonomous first-order differential equation dy/dx = y - y³ and the initial condition y(0) = y₀. Sketch the graph of a typical solution y(x) when y₀, has the given values. (a) y₀ > 1

A cell culture contains 9 thousand cells, and is growing at a rate of r(t) = 4e^0.24t thousand cells per hour. Find the total cell count after 2 hours. Give your answer accurate to at least 2 decimal places.

In 2012, the population of a city was 6.69 million. The exponential growth rate was 3.15% per year. a) Find the exponential growth function. b) Estimate the population of the city in 2018. c) When will the population of the city be 11 million? d) Find the doubling time. a) The exponential growth function is P(t) = ▢ where t is in terms of the number of years since 2012 and P(t) is the population in millions. (Type exponential notation with positive exponents. Do not simplify. Use integers or decimals for any numbers in the equation.)

Find the general solution of the given second-order differential equation. 25y" – 15y' - 4y = 0

Consider the following differential equation and seek a power series solution centered at x₀ = 0. (x² + 4)y'' - xy' + 5y = 0 (7) Upon initially substituting in, all FOUR series have the same exponent on x EXCEPT for one. The one that has a different exponent has an exponent of (A) n (B) n-1 (C) n - 2 (D) n+1 (8) The recursion formula for the coefficients is (A) an+2 = (n(n-2)+5)an/(4(n + 2)(n + 1)) (B) an+2 = -(n(n - 2)+5)an/(4(n + 2)(n+1)) (C) an+2 = (n(n-2) +5)an/(4n(n-1)) (D) an+2 = (n(n - 2) + 5)an /(4n(n + 1))

Using the method of Laplace transform. Solve the partial differential equation δu(x,t)/δt + u(x,t) = δu(x,t)/δx, u(x,0) = 6e-³x, which is bounded for all x >0; t>0; using the method of Laplace Transform.

The differential equation y' = 3x will produce which of the following? A. A slope field with parallel tangents along the diagonal B. A slope field that does not have rows or columns of parallel tangents C. A slope field with columns of parallel tangents D. A slope field with rows of parallel tangents

A 4-kg object's position, p, is changing with respect to time, t. The object experiences a force, F, that is proportional to the object's acceleration times its mass. What differential equation represents this dynamic? A. F = 4p' B. F = 4p" C. F = 4v D. F = 4t

Consider the following first-order initial value problem: dy/dt = 2y + t, y(0) = 0 (a) Compute the laplace transform to the both sides of the equation. (b) Substitute the initial conditions and solve for the Laplace transform of the equation. (c) Find the solution by taking inverse Laplace transform.

Consider the following first order initial value problem: dy/dt= = 2y +t, y(0) = 0 (a) Compute the laplace transform to the both sides of the equation. (b) Substitute the initial conditions and solve for the Laplace transform of the equation. (c) Find the solution by taking inverse Laplace transform.

Consider the following first order initial value problem: dy/dt = 2y + t, y(0) = 0 (a) Compute the laplace transform to the both sides of the equation. (b) Substitute the initial conditions and solve for the Laplace transform of the equation. (c) Find the solution by taking inverse Laplace transform.

No calculator is allowed on this question. y 3 - - 1 1 - 1 1 / - 1 - - / 1 31 1 13 1 1 / - / - - 1 1 1 - / 1 1 - 1 III - -3 The slope field shown above is for which of the following differential equations?

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