Let n > 1 be a positive integer. S[v] - [* da (y)"e", dx (y')" e, y(0) = 1, y(1) = A > 1, has a stationary path given by y = n ln(cx + e¹/n), where c = eA/n - el/n C Use the Jacobi equation to determine the nature of this stationary path.

Q: Express (x + 4/x)dy/dx - y = 1 in the form y = f(x) where the curves passes through the origin.…

A: Given differential equation : x+4xdydx - y = 1                    ...........( 1 ) Multiplying both…

Q: find dy/dx at the given point. (x + 2)2 − 6(2y + 3)2 = 3, (1,−1)

A: Given that  (x + 2)2 − 6(2y + 3)2 = 3 Differentiating with respect to x

Q: Express the equation in Heaviside Function

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Q: dy y = x-'(a² + x²)¿, solve for dx

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Q: Find dy/dx and d²y/dx2 for r = t2 +t +1 and y = t2 + 2t - 1.

A: given that x=t2+t+1 and y=t2+2t-1 we have to find dydx and d2ydx2 Now,          dydx=dydtdxdt…

Q: Find the directions in which the function f(x,y) = x²y + e* sin(y) Increase and decrease most…

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Q: Find the directions in which the function f(x, y) = x²y+exy sin(y) Increase and decrease most…

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Q: what is the dependent variable and linearity of the DE: d(xy)/dx + xy=0?

A: We will find out the required values.

Q: Which of the following functions satisfy x²dy+ y(x + y)dx=0 with y(1) = 1 ? 3x²y = x+y 3x²y = 2x-y…

A: Given the differential equation: x2dy+yx+ydx=0 with y1=1 To find out which function satisfies the…

Q: Find the linearization of the function a) z = cos(sin y – x); at (-2,0) and use it to approximate…

A: Suppose f(x,y) be a differentiable function at (a,b). Then linearization of f(x,y) at (a,b) is given…

Q: (3) Sketch a curve y = f(x) that satisfies: f(0) = 3, and dy dx -2. What is f(x)?

A: The function y=fx that satisfies f0=3, and dydx=-2. We have to find fx and sketch its graph.

Q: find dy/dx if x=(t2-2t+1)e3t and y=(t2+4t+4)e3t

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Q: Find a family of solutions for x2y dx +(x2-x)dy=0. Assume x>0

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Q: (ii) y = e2x cos(1+2x²) (1+2x²)

A: y=e2xcos1+2x21+2x2

Q: Find the function y = f(x) whose graph passes through the point (5π/12,3.5)if dy/dx =cos(2x−π/3).

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Q: Let y || dy dx = 9x-2 + 4x-¹-7. Find y if y(1) = 8.

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Q: Find a family of solutions for x2y dx +(x2-x)dy=0. Assume x>0

A: Given differential equation is: x2y dx + (x2-x) dy=0x2y dx=(-x2+x) dy This given differential…

Q: Find y as a function of tif y(3) = 8, y'(3) — 9. Y - 49y"+126y + 85y = 0,

A: Find  as a function of  if  ,  .

Q: 4-3x Consider the function y=e¹-3. Find y'.

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Q: Use the chain rule to help you find dy/dx for each of the following functions: 10. y = (x²+4)³ 12. y…

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Q: Find a > 1 to express y = 3(2/9)x in the form y = 3(a−x)

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Q: Are the functions f, g, and h given below linearly independent? f(x) = et – cos(5æ), g(x) = e* +…

A: The functions are linearly dependent :

Q: Graph the slope field for the equation dx/dy = -x(x2-4) and attach it to the solution. Draw (by hand…

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