Consider the solution of the ordinary differential equation                      y'(x)=-y3 +y2 +2y  subject to y(0)=y_0 in (0,2) , then lim(y(t)) as t tends to infinity. a. {-1,0}   b.{-1,2}  c.{0,2} d.{0, infinity}

Q: Suppose f and g are differential functions with the values given below. f(x) f'(x) g(x) g'(x) 1 1 3…

A: The answer is found in step-2

Q: 6. The final answer to the following question is incorr Tell me, in your words, about the mistake…

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Q: 7. Determine the singular points of the differential equation below. Also, classify them as regular…

A: Singular point:-  A singular point of the DE   a2x y''+a1xy'+a0xy=0  is any   point x,  s.t.…

Q: 1. Find the derivative of f(x)= x(a+1), given a is a constant.

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Q: 12. Sketch a direction field for the differential equation y' = xy+y, from -4 to 4. Then use it to…

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Q: 79. Suppose that f(x) satisfies the following equation (an example of a differential equation):…

A: Consider the differential equation

Q: 6. Find the total differential for the following equation of the following equation; z = ex² + y²…

A: We Know that  For function z = f(x, y) whose partial derivatives exists and  Total Differential of z…

Q: 3. Find the value(s) of k for which y = e satisfies the equation y+2y' = y" derivative) (note: y" is…

A: k = 1+2, 1-2explanation is given in below step

Q: Let f and g be two functions having continuous second derivative on the interval [a, b). Its given…

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Q: h(x)=2x^4+5x^3+29x^2+80x-48  Zero:-4i The remaining zeros of h are

A: h(x) = 2x4 + 5x3 + 29x2 + 80x - 48 We know, if a complex number is a zero of a polynomial, then its…

Q: sec y Obtain the solution of the differential equation y' x-4x+5 a. 2 sin y = In(x² – 4x + 5) + C b.…

A: ∫cosx=sinx +c∫dx1+x2=tan-1(x)+cCosx=1secx Given D.E y'=sec(y)/x^2-4x+5

Q: 6. Calculate the derivatives of the following functions. DO NOT simplify the answers! a) g(x)= In…

A: Please refer the attached image for complete solution.

Q: D. Fina the total differential of the function xye¬(x²+y*),

A: Given: f(x,y)=xye-x2+y2

Q: 5. Find all the first and second order derivatives of the function f(x, y) = x³ ln(y) + ³xy + x²y³ +…

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Q: consider the differential equation dy/dx=sin(x)/y for which the solution is y=f(x). Let f(0) = 1…

A: Given dydx=sinxy, y0=1. By variables separation,  y dy=sinx dx Integrating on both sides,

Q: d. y= x² + y x + cos y

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Q: If the differential equation y" +y' – 6y = 0 has a primitive function y = e , where r e R, then the…

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Q: Obtain the differential equation associated with the given non-derivative equation in x and y. Show…

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Q: (a) State the definition of the 'usual' differential of a function F(x). (b) Use the relation F(x +…

A: Definition of the differential function of F(x):   Part (a):   Let the function F(x) is continuous…

Q: Show that if the roots of the auxiliary equation of a differential equation are r = p± qi, then the…

A: The given roots are r=p±qi. Show that the differential equation itself is y''-2py'+p2+q2y=0. Here we…

Q: 1. Find the general solution for the following differential equation. a. y'= 2y - 4x

A: You have posted multiple question which are not interlinked and i can solve only one question as per…

Q: 27. Let g be a function such that g(y) > 0 for all y. Which of the following could be a slope field…

A: ( If you want more explanation please let me know).

Q: 20. Given the differential equation dy= x*dx, find .2 %3D the equation of “y" in terms of “x" as the…

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Q: 1. Express the general solution of the given differential equation on the interval (0, 0) in terms…

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Q: Find the solution to the given equations: (a) y" + y' – 2y = cos(x) – 3 sin(2x), y(0) = 1, y'(0) = 2…

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Q: 7. Find a linear differential equation with constant coefficients Ly = 0 such that y(x) = cos(x) +…

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Q: 17. The integrating factor to the linear differential equation x(x? +1)y' +2y = (x² +1)³is: x2 x? a.…

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Q: Find an integrating factor and solve the given equation. (15x²y + 2xy + 5y³) dx + (x² + y²) dy = 0.

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