solve the SDE dX = − 1 /τ( (X − µ)dt) + (2D)-1/2 dB. X(t =...

solve the SDE dX = − 1 /τ( (X − µ)dt) + (2D)^-1/2 dB. X(t = 0) = β

Expert Solution

Colby Messinger answered 2 years ago

2) Solve the system of equations below dx/dt – 3x – 6y = t^2 ...

2) Solve the system of equations below dx/dt – 3x – 6y = t^2 dx/dt + dy/dt – 3y = e^t

Solve the given initial-value problem. dx/dt = y − 1 dy/dt = −6x + 2y x(0)...

Solve the given initial-value problem. dx/dt = y − 1 dy/dt = −6x + 2y x(0) = 0, y(0) = 0

Use a LaPlace transform to solve d^2x/dt^2+dx/dt+dy/dt=0 d^2y/dt^2+dy/dt-4dy/dt=0 x(0)=1,x'(0)=0 y(0)=-1,y'(0)=5

dx dt =ax+by dy dt =−x − y, 2. As the values of a and b...

dx dt =ax+by dy dt =−x − y, 2. As the values of a and b are changed so that the point (a,b) moves from one region to another, the type of the linear system changes, that is, a bifurcation occurs. Which of these bifurcations is important for the long-term behavior of solutions? Which of these bifurcations corresponds to a dramatic change in the phase plane or the x(t)and y(t)-graphs?

Solve the system of equation by method of elimination. dx/dt + x−5y = 0, 4x +dy/dt+...

Solve the system of equation by method of elimination. dx/dt + x−5y = 0, 4x +dy/dt+ 5y = 0, x(0) = −1, y(0) = 2.

Solve the following integral ∫ (x^2 + x + 2) / (x + 1)(x^2 + 1) dx....

Solve the following integral ∫ (x^2 + x + 2) / (x + 1)(x^2 + 1) dx. Use partial fraction decomposition. Show all work and steps to get to solution.

Assume x and y are functions of t. Evaluate dy/dt with 4xy-5x+6y^3=-126, with dx/dt=-18, and x=6,y=-2...

Assume x and y are functions of t. Evaluate dy/dt with 4xy-5x+6y^3=-126, with dx/dt=-18, and x=6,y=-2 A retail store estimates that weekly sales and weekly advertising costs x are related by s=50,000-30,000e^-0.0004x. The current weekly advertising costs are $2,500, and these costs are increasing at a rate of $400 per week. Find the current rate of change of sales per week. Use implicit differentiation to find y’ for the equation below and then evaluate y’ at the indicated point, (-4,4)....

1. Consider the following second-order differential equation. d^2x/dt^2 + 3 dx/dt + 2x − x^2 =...

1. Consider the following second-order differential equation. d^2x/dt^2 + 3 dx/dt + 2x − x^2 = 0 (a) Convert the equation into a first-order system in terms of x and v, where v = dx/dt. (b) Find all of the equilibrium points of the first-order system. (c) Make an accurate sketch of the direction field of the first-order system. (d) Make an accurate sketch of the phase portrait of the first-order system. (e) Briefly describe the behavior of the first-order...

Solve (1+e^x)dy/dx+(e^x)y=3x^2+1 Solve (x^3+y^3)dx+3xy^2 dy = 0 Solve (y-cos y)dx + (xsiny+x)dy = 0 Solve (1+ln...

Solve (1+e^x)dy/dx+(e^x)y=3x^2+1 Solve (x^3+y^3)dx+3xy^2 dy = 0 Solve (y-cos y)dx + (xsiny+x)dy = 0 Solve (1+ln x +y/x)dx = (1-lnx)dy Solve (y^2+yx)dx - x^2dy =0 Solve (x^2+2y^2)dx = xydy Solve Bernoulli's Equation x dy/dx + 2y = (x^4)(e^x)(y^2) Solve Bernoulli's Equation (1+x^2) dy/dx = 2xy +(e^x)(y^2) Solve IVP (3e^(x^2))dy + (xy^2)dx=0 ; y(1) = 2 Solve IVP dy/dx -2xy = e^(x^2) ; y(0)=0 Solve IVP (x^2+y^2)dx+(2xy)dy=0; y(1)=1 6. Mixture Problem Initially 40 lb of salt is dissolved in a large...

Solve the given system of differential equations by systematic elimination. 2 dx dt − 6x +...

Solve the given system of differential equations by systematic elimination. 2 dx dt − 6x + dy dt = et dx dt − x + dy dt = 3et

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