30.3. Find and classify the isolated singularities of the following func- tions: +1 Z sin 3z (a). (b). 2²e¹/2, (c). (d). z²(z - 1) 2 COS Z (2²-1) COS TZ (e). cos (f). (z+ 2) (2z -1) (z² + 1)² sin² z 7 1 sin(z − 1) z z² +1

Q: A second order Caushy – Euler equation having a solution y(x) = x-cos(4Inx) is O x²y" + 5xy' + 16y =…

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Q: 1. If x'y" + xy' + (x². 4 - -y=0 Y=x sinx , and y= y,v. Which of the following x>0 equations…

A: Solution:    Given:                  x2 y"+ xy' +(x2 14) y =0, x.o                 y1 = x-12…

Q: 2.) If H (y) = cos y – sin y, find H (0), H (n),H (T), and also show that H. n+ x) = H (n - x) = -H…

A: The solution is given as

Q: 3. Find and classify the isolated singularities e¹z sin² (a) f(z) = 1 2 (b) g(z) = = sin z 22 - z

A: Given that find and classify all isolated singularities.   a f(z)=e4z-1sin2z,     (b)…

Q: (c) Given T" = 6x²y³ – cosx + 5y² – siny + 10x² – e-3x," determine (1) T' = S(T")ax T' = S(T")ay…

A: GivenT"=6x2y2-cos x+5y2-sin y+10x2-e-3xwe know…

Q: 2. Which of the following is correctly matched? O z'y" - e"y" + sin r(y') = 0: linear, third order O…

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Q: 7. Set f(x) (a) (b) (c) (d) = 2 +4 8 cos 2x, 2sin2, + e-8/2 s² + 4 S s² +4 8 8² +4 (e) None of the…

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Q: Find az/ax and dz/dy. xyz + cos(xy) - 2y sin(x) + z² = 3 Find az/ax and dz/dy. exz ZX y

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Q: 7. Find the rectangular equation if r = 4 cos 0 + 4 sin 0 (a) (c) x² + y² = 4 x² + y² = 4(x + y) (b)…

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Q: 2. (Cauchy-Riemann's equations, analyticity and harmonic functions) (a) Define the symbols Of/0E and…

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Q: 1. F = cos y i+ xyj + yk, A B C D E F О н A. i+j+(y-siny)k B. i+ (siny - y)k C. j (2y-siny)k D. 3i -…

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Q: 32) Find ур(0) for the equetion y (4) - y" - 2y + 2y = 3xe³ + cos x

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Q: 3. Solve the IVP: siny(x + siny)+2x²cosy y'=0; y(-1)= π/2 (Subst. first and then Bernoulli's)

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Q: 5. If xy + 3y2 = 2, evaluate the values of (a) y at the point (-1, 2) and b Find dy for the…

A: Given: (a) To evaluate y' at the point (-1, 2), (b) To find the derivative dy/dx?

Q: 5. Find L{f(t)} a. f(t) = sin?(t) + t b. f(t) = n² – 8e¬2t + (et + 1)² | c. f(t) = F, sin yt -cos…

A: As per our limit we can solve only first three subdivisions if you want the answer for other…

Q: 10. Solve for t on the interval [0, 2π) (a) 2 cos² t-cost-1=0 (b) 2 sin²t-3 sint + 1 = 0 taol al (c)…

A: Given

Q: : Mark all the ODEs in the list for which the function y(t) = cos(t) is a solution. A) y' = sin(t)…

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Q: # 8.) (8 # dy + Bernoulli s D.E, dx - 3xy2 dx =0> DET. THE GEN, soL'N OF THE D.E.

A: As we know that; The standard form of Bernoulli's equation is; dydx+Py=Qyn Where; P& Q is the…

Q: X. 1. (D² )y: 2. (D² + D)y = cos²x+ sin²x² 3. y// – 2y/ + 2y = e¯*cosx 4. y// + 4y + 3y = x – 1 5.…

A: Given The given differential equations are (3) y"-2y'+2y=e-xcosx (4) y"+4y'+3y=x-1 (5)…

Q: 2.) y"-3y'+4y = sint ; y(0) = 0, y' (0) = 1 The answer should be: (1/6)cos t + (1/6)sin t -…

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Q: 5. The following DE are exact except (A) 2ry³ +e+(3.x²y² + sin y)y = 0 (B) 6.ry² + 2y + (9m²y² +…

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Q: (4) find dy if 3って - ソ= e* (2Co83x +3Sin3x) e = Sin (x+3y).

A: Given 1. y=e2x2cos3x+3sin3x 2. e2x=sinx+3y

Q: Let Ур be the particular solution to the nonhomogeneous ODE. Choose a suitable trial solution, of…

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