The time rate of change of liquid circulating in two tanks is govemed by dy -0.02x + 0.02y, = 0.02x – 0.02y, %3D dt dt x(0)%3D0,y(0)%3 150, detemine x and y at t =0.1 using Runge-Kutt method.

Q: 3. Apply Euler-Maruyama method as one step to solve the SDE 3 y dy dt + dBt 5 t y(1) = 2

A: Given dy=3-y5-tdt+dBty1=2

Q: Find the differential dy of the given function. y = V4 - x2 dy =

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A: Given family of Curve is x2-3xy-2y2=C

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A: Since you have posted multiple question we are supposed to give solution of first one only ...kindly…

Q: Solve the initial value prol dy + 8, y(1) = 3 dx y%3D 4 Jx +8x 19 4 Oy=Vx + 8x - 6 Oy=-- - 8x- 6

A: Explanation and solutions is given below....

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Q: Find y(2) and yG) For fundion yft) that saticFies initial-valve dy +2 dy +y dt =2+ (t-3) 6 Ult-3) ;…

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Q: dy 3; find dt dx when x = 2. dt Related Rates: Given y = x³ – 2x and %3D

A: As we know that; The Power Law: ddxxn=nxn-1 From the given problem: y=x3-2x ; dydt=3 First, we have…

Q: Find the differential dy of the given function. y = InV9 - x2 dy =

A:

Q: Approximate the solution of dy _ y-1 dx x+3 %3D with initial condition y(-1)=0 for –1<x<0 by using…

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Q: dy at x = 1 if y = 4x² + 1 and dt dx Find – 1. dt dy dt || ||

A: Solve the following derivative

Q: 1. Use the Improved Euler's method to integrate dx = t - sinx dt given x(0) = 1, using a step size…

A: The given differential equation is dxdt=t-sin(x), x(0)=1, h=0.1 The formula for improved Euler…

Q: (a) Find the solution to dy: dt dyz Y1 + 3y2 3y1 – V2 dt with the initial condition y1 (0) = 3,…

A: Solution a: Given system of differential equation is dy1dt=3y1-y2dy2dt=y1+3y2 with initial condition…

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Q: Find  dy/dt  using the given values. y = x3 − 9X for x = 3,   dx/dt = 2. dy dt =

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Q: dy Kutta method to integrate = 4e0.8x step size of h 0.5 and an initial condition of y = 2 at x =0…

A: 4th order Runge-Kutta method…

Q: A particle moves on the circle x2+y2=25 in the xy-plane for time t≥0. At the time when the particle…

A:

Q: 4. Find the double integration of [(1+xy* )dx dy. ww m

A: The given integral is ∫04∫y2y(1+xy2)dx dy

Q: An object is being heated such that the rate of change of the temperature T in degree Celsius with…

A: Here we have to use the Runge-Kutta 4th order method

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Q: Use Picard's Iteration Method to find the solution of- = t - y? up to third dt approximations when…

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Q: # 5) If y = x³ + 2x and dx/dt = 5, find dy/dt when x = 2. # 9) If a snowball melts so that its…

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Q: 2. Find dy/dx a) y = dt, x> 0

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Q: Suppose that a body moves through a resisting medium with resistance proportional to its velocity v,…

A: (a)

Q: Use a computer algebra system to graph the slope field for the differential equation and graph the…

A: The differential equation is dydx=0.8y, y(0)=4. Solve the equation as follows.…

Q: dy Use 4th order Runge - Kutta method to integrate step size of h = 0.5 and an initial condition of…

A: Let dydx=f(x,y) and the initial condition is y0=f(x0) . The 4th order Runge-Kutta method uses the…

Q: Find all the critical points (equilibrium solutions) of dx dy = y+ 5xy. dt dt

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Q: Solve y(1): dy/dt + x = 1; dx/dt-y + 4e¹ = 0; x(0)=0 and y(0)=0.

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Q: he given initial-value problem. dx = y - 1 dt %3D dy -6x + 2y dt x(0) = 0, y(0) = 0 0, у (0) %3D 0

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Q: Solve the IVP dy/dt + 2(t + 1)y^2 = 0, y(0) = −1/8

A: To solve the IVP dy/dt +2(t+1)y²=0, y(0)=-1/8

Q: 2. Use the 4th-order Runge-Kutta method to integrate dx = t - sinx dt given x(0) = 1, using a step…

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Q: a) dx dt dy dt =x+√3y+et √3x-y+e³t = ||

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Q: 1. y(4x + y)dx – 2(x² – y)dy = 0

A: We will first convert the equation to exact and then solve

Q: Use Euler's Method with a step size At = 0.1 to estimate y(0.5) given that (x(0), y(0))= (1,1) and…

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Q: What is the solution of given initial value problem? d²x = y + sin t dt2 d²y dx + cost dt dt2 æ(0) =…

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Q: Create a slope field of the differential equation dy cos(t) + cos(y) dt and draw solutions…

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Q: Use the fourth-order Runge Kutta method to solve for the velocity and position of the free-falling…

A: Given:- t=0 , x=v=0  t=4s

Q: (a- Use Euler's method to integrate dy = y – t² +1 dt from t=0 to 0.2 with a step size of 0.05. The…

A: Note: As per bartleby instruction when more then one question is given only one has to be answered.…

Q: Find the differential dy of the given function. y = V4 - x2 dy

A: Consider the given function. The problem requires to find the differential dy of the given…

Q: d²x dx + 4 + 5x – 10 = 0, when t dt 0, x = 0, x = 0 %3| %| dt2

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Q: dx 2x - y dt dy

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Q: Use Euler's method to numerically integrate dy -2x3 + 12x2 – 20x + 8.5 %3D dx from x = 0 to x = 0.5…

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Q: Create a slope field of the differential equation dy = cos(t) + cos(y) dt and draw solutions…

A: Given: dydt=cos(t)+cos(y) To find: Slope field To sketch: The solutions corresponding to y(0)=0.5,…

Q: d²x dx + 4- + 5x – 10 = 0, when t = 0, x = 0,x = 0 dt2 dt

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Q: What is the differential equation of the orthogonal trajectories of the family of curves X2 -…

A:

Q: Consider a disease that propagates according to the system dx 3 357 — Зху — Зх dt - dy = X dt х*у —…

A: Given that, dxdt=357-3xy-3xdydt=x2y-13xy-68y The equilibrium points are,…

Q: 3. Apply Euler-Maruyama method as one step to solve the SDE 3 y dy = dt + dB 5-t y(1) = 2

A: Given the SDE is dy=3-y5-tdt+dBty1=2

Q: 8. Find the solution y(t) of th d³y dy - 2y% = dt dt3

A: