(x1) Solve the IVP: y/ , y (0) = 1 y2 O y22y( 1)3 9 O 3y2 6y 2 (x + 1)3 7 O y22y

Q: Solve the pollowing: り ( 2+J(xtjy) X=? ye! (b) (2+j)(3-j2) = a+jb a:? b:? (C) (メ-j2y) -(y-jx)-2j x=?…

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Q: Solve: x'y" - 7xy' + 41y =0

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Q: Find all functions y satisfying y" + y" = y' + y. You may use the factor- ization x + x² – x - 1 =…

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Q: Solve 4xx = ut + tx u(x, 0) = 0

A: The provided partial differential equation (PDE) describes a transport phenomenon represented by the…

Q: Express f(z) = x-1-iy (x−1)² + y² in terms of z.

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Q: Solve P(a-y) =1+(m/3) for y

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Q: (d) 12 2

A: Given, A=132-1

Q: Solve For the orthogonal trajectories (a+x) y² = x² (3a-x)

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Q: Let Y(t) = be the solution of , 6 1 Y, 5 4 -2 - Y' Y(0) 8 Write x(TT/10), round your answer to two…

A: To solve this problem first we write the system as a system of linear homogeneous differential…

Q: dy (y2+In2)=-(23+) %3|

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Q: 11. y = 5 3 * tn() 15 2x А. Inin 8 (35 С. Inin 15 (3" g") 2/x В. 15)(15) D.

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Q: d?y dx3 Solve - 27y=0 O a. y = ce -3x + e7*(c2cos- 3/3 x+C3sin 3/3 -x) 2 Ob. OBy=c,e3x +e"(c,cos 33…

A: We have to solve given problem:

Q: @3Dy+12 D3=24

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Q: Utt u(x, 0) ut (x, 0) = = = 4uxx x² + 3x

A: USIND D'ALEMBERT'S SOLUTION FOR ONE DIMENSIONAL HOMOGENOUS WAVE EQUATION ,WE HAVE

Q: (r2+2rt-4t2)dr-(r2-8rt-4t2)dt=0

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Q: Solve the IVP: X' = AX, where -2 1 A = -5 0 3 -2 and -2 X(0) = -1 2

A: To find the solution of X'=AX where, A=−210−50003−2X0=−2−12

Q: Solve for ‘x’ and ‘y’ where x + y = a – b, ax – by = a2 + b2

A: To solve the equation for x and y.

Q: Express ƒ(z) = 4x² + i4y² by a formula involving the variables z and ž.

A: Let,

Q: (x? + 3x — 45)dх J«+ 3)(х + 12)(4х — 3)

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Q: Find the differentiate

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Q: (3x*-5)(2x +9x-6 of y= dy and %3D Determine the 7x

A: Simplify the equation. y=6x7-10x3+27x5-45x-18x4+307x5=67x2-107·1x2+277-457·1x4-187·1x+307·1x5

Q: 23. (1.4) Solve y +2 = (4x + 2y + 6)-'e2«+v+3.

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Q: Ify= (x³ + 1)“ , theny = ? (A None of the given choices B(3x2)? © 2(x³+ 1) O 6x²(x³ +1) E 2(3x² + 1)…

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Q: What is the value of x in (2x - jy) + (y - jx) = 1 - j5?

A: We have to find the value of x where 2x-jy+y-jx=1-j5

Q: Q3 Find f-(x) for the following : 1- y = Jx-3 2- y = (2x³ + 1)'/5

A: For finding the inverse, we will replace x with y and y with x

Q: Example: Solve xy(2dx+ dy) = 2(3xdx+ ydy)

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Q: Solve: dz + 4x = yº O 11r¹y+y¹¹ = C O 1lry - y¹¹ = C O 11xy + y = C O 11x¹y - y¹ = C

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Q: (xdx ydy + zdz)2z {(z²x²y²) (xdx + ydy + zdz) dz + %3D

A: Differential equation

Q: Solve for the particular solution: x²y" - xy' - 3y = In x. Oyp = (In x)/3 - 2/9 yp = -x/3 + 2/9 Oyp…

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Q: Solve: (3x? – 2xy+ 3y² )dx = 4xydy O (y – 3x) (y + x) = Ca³ O (y + 3x)³(y – x) = Ca³ O (y – 3x)(y +…

A: Proceed as shown below

Q: differentiate the following: Q(y)= y3/3 + 3/y3

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Q: solve (3-2) dx Ex Solve 3xý = zy (y-3) Ex6 + (3x-4) dy =0 %3D

A: According to the guidelines issued by the company We are supposed to answer only one question.…

Q: f(x) = e−x,    n = 5

A: Given:          fx=e-x ,n=5 A Maclaurin series is given by fx=∑n=0∞fnan!xn Here fx≈Px=∑n=05fnan!xn…