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

Q: Sketch the graph of the parametric equations x = sint, y = 2 cos(3t), π ≤ t ≤ 27. Clearly label the…

A: We are to sketch the graph of the parametric equationsx = sint, y = 2 cos(3t), π < t < 2π.…

Q: Determine the singular points of V-2 -4+ I 1 (x+5)39: Classify each singular point as either regular…

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Q: 4. Find L cos t +t² – 3e¬9t + 5

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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: Find indicial equation at each regular singular point of 2.x (1+x) y" + (3+ x) y' – xy = 0.

A: The given equation can be written as:

Q: write answer as fraction -(1/2)^3

A: We know , (a/b)n = an/bn

Q: 7.2.1 Show that a quadratic form ax² + bxy + cy² may be converted to a form a'x¹2 + b'y2 by suitable…

A: Quadratic curve is of the form,substitution is given as

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: 4. Locate the fixed point of x = xy y = x + y and compute the index about the fixed point.

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Q: Find the singular points of the ODE and determine if each singular point is regular or irregular. a.…

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Q: If a field K is algebraically closed, then every polynomiel with co efficients in k has a root in K.…

A: A field K is said to be algebraically closed if every polynomial with coefficients in K has a root…