1. Find all singular and all ordinary points of the DE 2x²y" + 17xy' + 5x²y = 0

Q: 2. Show that the singular points of each of the following functions are pole Determine the order of…

A: Sinec the questions contains many subparts.As per the guidelines I am answering the first three…

Q: 8. Find the equation of the parabola ax? + by? + cxy + dx + ey nat passes through the points (3, 1),…

A: A parabola is given by, ax2+by2+cxy+dx+ey+f=0. Also the parabola passes through the points 3,1 and…

Q: 2. Consider the equation 2x³ + 5x – 4 = 0, 0 < x< 1. i) Show that by using Newton's formula, the…

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Q: Q2/ fincd lachre trans form for at X- 3x+2X=lee

A: given equationx"-3x'+2x=1-e2tby assuming that initial condition is zero.x"=s2X(s)and x'=sX(s)and…

Q: Q.5. Find all roots of x-3x-230using Cardano's formula.

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

A: Use the definition

Q: . Find the general solution of the first-order equation y? – 2ry dy dr

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Q: Solve by Cauchy euler the following equation

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Q: Convert 1 √₁-x² √(1-x² - ₁₁² ₂ = ( x ² + 1 ² + 2 ² ) {/² e -x² -√√1-x² - y² dz dy dx in spherical.

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Q: Find all singular points of the given equation and determine whether each one is regular or…

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Q: Solve the following Euler-Cauchy type equation: 1 (2²D² + 3xD+ 1)y %3D (1 – x)²'

A: The given ODE is given as: x2D2+3xD+1y=11−x2

Q: An equation of the form ty" + aty + By = 0, t > 0, where a and B are real constants, is called an…

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Q: 6у" + 26у — 0, y(0) = 9, у (0) — 4.

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Q: tions. Find the General solution of y" - 2y' + 5y = 4tet with Real valued func-

A: We have to find the general solution of the differential equation.

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: 39. Show that the graph of r =t sin ti + t cos tj + t'k lies on the paraboloid z = x² + y².

A: Here we compare r as its basic equation to prove this.

Q: . Find the real coefficients a and b such that the function u = 4r +4r'y+ar y² -4ry+by is harmonic…

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Q: 3. Find the residues of the functions 1- cosz а.) b.) c.) z'e at z=0; .5 e -1 and express the types…

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Q: Classify the equation (n-1)²Zxx - y²nZyy = ny²n-1zy and reduce it to a canonical (normal) form.…

A: As per the question we are given a partial differential equation and we have to :Classify the given…

Q: 10. Subtract 2- V- 64x²y* from – 3– xy-9y' and express the result in a + bi form

A: Answer and explanation is given below

Q: Which of the following functions do not form a set of fundamental solutions of y" - 4y 0 Select one:…

A: We will find out the required set which don't form a fundamental set of solution.

Q: 3. Find the fundamental set of solutions of the DE y"" + 4y = 0.

A: Given DE  is  y"'+4y'=0 Now the auxiliary equation , after putting y=emx in the above DE, is given…

Q: 4. Find the Differential Equation and Orthogonal Equation of the family of parabolas with vertex and…

A: Let the vertex lies at (a,0) and focus at (b,0) So the general equation of parabola having axis as…

Q: 2y )dx - (x +3 cos y)dy around the parallelogram havi - 6

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Q: 1. Find all singular and all ordinary points of the DE (0.5x²+2x+25)y"+xy'+y=0

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Q: cracks between descending powers of x or a. Study the exa. Zx²-5xytyz wy – 3xy + y' sy +y 5. 280 + y…

A: Given that : 280+y+x+3y-2y+x. We will re-arrange the expression by taking the x terms and y terms…

Q: Find all the regular singular points of (4 – x2)y" + 2xy' + 3y = 0 by using the definition.…

A: The given question is solved below.

Q: Which of the following is not Cauchy-Euler equation? Lütfen birini seçin: a. 3t°y" + 2ty' = sint +…

A: The general form of the Cauchy-Euler equation is: antnyn(t)+an-1tn-1yn-1(t)+...+a0t0y(t)=0 Here, the…

Q: Which of the following is a fundamental set of solution of y" – 2y' + 5y = 0.

A: