Question 2. Find and classify the singular points of the DE as regular or irregular. (4 Points). а) (х — 2)(х — 3)у" + ху' +. y = 0. (x-3)² x* c) (x+ 1)(x – 2)y" + xy' +; x2 (x+1)2Y = 0 b) (x – 2)(x – 3)y" + xy' + y = 0. (x+3)² d) (x + 1)(x – 2)y" + xy' +; (x-1)2 x² y = 0

Q: Eliminate the arbitrary constants of the equation y = ce-2x + C2e3x (A) у" - 4y' - бу 3D0 в) у"- у -…

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Q: 3. Classify the stationary points of (a) f(r, y, 2)= x² +x*y+y*z+ – 42 (b) /(2, 23, re)- 20xy…

A: a) stationary point of f(x, y, z):-At those points where∂f∂x=0,∂f∂y=0,∂f∂z=0…

Q: Determine the singular points of (x² – 9)?y" + (x + 3)y' + 2y = 0 and classify each singular point…

A: Use the definition

Q: 2.The equation of C3 can be expressed as z=p+qi+ce^iθ, where θ varies from mπ to nπ. What is the…

A: Given: A semicircular path from 0,0 to 2,2 denoted by C3. The equation of C3 can be expressed as…

Q: 2. Solve for y in terms of x for the following equations: a) In(1- 2y) = x %3D b) In(y- 1) - In 2 =…

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Q: (b) (2, -5π/6) (r, 0) = (r, 8) = y -1 -2 -3 -5 -1.5 (r> 0) ] ) (r< 0) 1 -1.0 2 3 -0.5 4 y -0.2 -0.4…

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Q: 6. Show that when 0</z - 11 < 2, Complex Analysis (z-1)" (2-1)(2-3)=-3 (2- #=() 2(z-1)

A: Here we prove this statement by using series expansion.

Q: In the coordinate plane, right triangle AXYZ is reflected over the line y = x. 5 3 X 2- -6 -5 -4 -3…

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Q: Which of the following is the general form of a homogenous equation? A a, (x)y"…

A: The objective of the question is choose the correct option.

Q: 2- x3(x-1)y" + (x-1)y' -4xy =0 3- x2(x2-4)y" +2xy' -3y =0 4- x*y" + y =0

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Q: If u = x² tan equal to (a) (c) x - y x + y - 2 + V² 2 X X -, y x + y x - y x² + y² 2 X - y - y² tan…

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Q: (16) Show that: (1) The function f(z) is continuous in all complex plane. (2) (-1+i)-8(1+i).

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Q: Solve for x: xy2 + yz2 - 4 = 2x - 1. 3-yz2 b) х %3D у2-2 a) x = *y^tyz2-3 2 с) х %3D 3 — yz2 -у? +2…

A: Consider the given expression.

Q: a) 12 Q.7) To write the power series £=3 4m as the form -4m a) m - 1 we must shift m to become : d)…

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Q: 3) y`+y=xe*

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Q: • Solve the equation using homogenous equation (5v-u)du + (3v - 7u)dv = 0 a.)(3v +u)² = c(v - u)…

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Q: 1. (r - x) + (-2r + 3x) 2. (-y + 3) - (v - 2) 3. (-3a* + 4 + 2a') -(2 + Sa - a) 4. -(6 - b + 4b')…

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Q: y"+y' + (a) -5 x-b = 0, Xo = 2 is 5. (b)-3 (c)-2 d)-8 Q7) L(y") = a) s²L(y(x)) + sy(0) - y'(0) c)…

A: We have given the answer in the next step. Hope you understand that

Q: the exponents at the singular point x=2 (the roots of the indicial equation) for (x – 2)2(x + 1)y" +…

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Q: Q1:- A) solve the following D.E '5 x?y" + 1 - B):- у" + у' — бу %3D 8е3х

A: Since you have posted a multiple question ,I will solve the first question  for you. To get…

Q: Suppose a point P with coordinates (x,y) is reflected in the x-axis and then its image P'  is…

A: The objective of this question is to find the coordinates of a point after it has been reflected…

Q: 6) Use Linear Property to find ( 1- 3 x4)' A) (1- 3 x4) %3D B) – 4x3 C) - 2 D) - 12 x3 7) Use…

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Q: . Let complex numbers a and 1/a lies on circles (x – xo)² + (y – yo)² = r² and (x- x)² + (y – yo)² =…

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Q: 5. y"+9у-0

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Q: The following series converge. Find their sums. 1 7. 2n-1 n=1 3n+1

A: Consider the given series ∑n=1∞12n-1+23n+1

Q: 1 b)y" + y = ; 1+sinx

A:

Q: 3- x2(x2-4)y" +2x3y' -3y =0 4- x*y" + y =0

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Q: Prove that a parametric function given by I= 21 + 312 y = t² + 21 satisfies the equation dy + 2 dr…

A: see the details solution in below

Q: 16 4 2 -6 -4 -2 2 4 -2 -4

A: topic - relection of point about y=1 C'(2,4)

Q: 1. 4y" — у 3 10 2. (D3 + 2D?)у %3D— 4 3. уМ) — 4y" %3D х — 2

A:

Q: Use implicit differentiation to find 2x²y²-3y³ +52²=0 A) 4x³y 5z B) 5: C) ex 10 yz 4xy-9y2 +522 D)…

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Q: - فم( (x² – 4)²dx 6. -2 10x4 x3 1 + 15Vx3 – 7) dx 7. 2 3 dx 2x° + x4 8. 1 | (2x + 1)(x – 1) dæ - 9.…

A:

Vertices Of An Ellipse

In the study of the conic section of the geometry, An ellipse is a plane curve surrounding two focal points, or foci where the set of all locus of points in the plane has their sum of the distances to the two foci is constant. On the ellipse curve, it is the intersection point of the main axis. In an ellipse graph, the center of the axis is the midpoint of the line segment connecting the foci. The major axis is the line section that runs through the ellipse's foci, while the minor axis runs through the middle and is perpendicular to the major axis.. The ellipse has two endpoints on the major axis which are known as the vertices (in plural), vertex in the singular. The equation of the major axis is 2a, the equation of the minor is 2b and the distance between the major axis and minor axis is 2c. The semi-major axis has a length of a and the semi-minor axis has a length of b. The ellipse's vertices are determined by the elliptical orbit's equation and graph.