Let z=3+7i and w=7−8i . Find out the following in the x+iy form.

Q: (b) у" — 2у + у 3 еt sin(z)

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Q: find the general solution to the given Euler equation.Assume x > 0 throughout. x2y'' + 3xy' + 10y…

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Q: Show that the following gn are harmonic and find its conjugate u=3x^2y+2x^2_y^3_2y^2

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Q: Find the general solution to the given Euler equation. Assume x > 0 3x2y" + 4xy' = 0

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Q: Show that the equation dy_c² Ə²yXX 2 d +2k Ər² Ət əx² oro nobene possesses solutions of the form 00…

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Q: Exercise 3: Solve the following equation for x and y where 3 xy – 2i + x + 2xyi – 5 = -- 3i 2

A: Solution of the equation

Q: Which of the following is linearly independent? (a) 2sin?x & 1– sin?x (b) 4e2* & e-2x (c) 3sec?x –…

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Q: Transform the equation y + (ar - v + by = 0; y = Vau(x) Use given substitution and show that above…

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Q: Q11\ Express in the form x + (1) ei(a/2-j) (2) In(3– j) (3) sin(rt/ 4+ j2)

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Q: Find the imaginary component of In(z + w) if z = 16 + 6i and w=7+8i . Round off your final answer in…

A: Complex number, imaginary part

Q: The roots of a d.e are -1, 2tV3i What is the solution? O a. y = e*(c, cos 3x + c2 sin 3x) + c3 cos x…

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Q: Using complexification, find the general solution of d²y dt2 dy +2- + 5y = 34 cos 2t. dt

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Q: Find the general solution to the given Euler equation. Assume x > 0 4x2y" - 16xy' + 25y = 0

A: Given:4x2y"-16xy'+25y=0Cauchy-Euler:ax2y"+bxy'+cy=0amm-1+bm+c=0

Q: Write the general solution of the following Bessel equation 8x*y`+8xy`+(8x² – 72)y=0 a.…

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Q: 2. Let R(t) = } sin 4t î – bcos“(21) j + 2t k. E

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Q: Find the general solution to the given Euler equation. Assume x > 0 x2y'' + 2xy' - 2y = 0

A: Solution -  The given equation is of the form of -  ax2d2ydx2+bxdydx+cy = 0,               Euler's…

Q: 18 In(z – 3) Question 10) Find I = -dz, where C = Iz - 2 + 4i| = 4, Ccw z2 + (4 + 4i)z + 3+ 4i

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Q: Q1:-/ Verify by direct substitution that y, = epx cos qx and y2 = ePx sin qx , are solutions of the…

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Q: Find the general solution to the given Euler equation. Assume x > 0 x2y" + 6xy' + 4y = 0

A: Given information: x2y'' +6xy' +4y=0

Q: Find the general solution to the given Euler equation. Assume x > 0 x2y" - 5xy' + 10y = 0

A: Consider the provided differential equation, x2y''-5xy'+10y=0 Find the general solution to the given…

Q: Reduce the following equation to a canonical form and hence solve it: 3u +10u xy +3u vy = 0 xXx ху…

A: See the solution in the given fig.

Q: a. Solve the ODE y" + 3y + 2y = 0. b. Use the method of undetermined coefficients to find a…

A: We can solve the given differential equation using method of undetermined coefficients. In this…

Q: Yı = e', yɔ = sin2t, y3= cos2t make up a fundamental set of solutions by finding the Wronskian.…

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Q: find the general solution to the given Euler equation.Assume x > 0 throughout. x2y" + 7xy' + 13y…

A: The Euler equation is given by  x2y" + 7xy' + 13y = 0 To find: General solution to the given Euler…

Q: Find the general solution to the given Euler equation. Assume x > 0 x2y" + 7xy' + 13y = 0

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Q: 1. a) Find , if y= (x² – 11)“ dx b) Express (8/30) (2Z60) in the form a+ bi c) Solve (2+3) +3/- x+iy…

A: The detailed solution is as follows below:

Q: Exercise 3: Solve the following equation for x and y where 3 xy – 2i + x + 2xyi – 5 =- 3i | 2

A: This kind of problem we can solve by comparing the real and imaginary parts and after that solve the…

Q: Evaluate the complex integral e19.1.png rx+yi dz az + b if a = 2, b = 6, c= 17, x = 1, and y = 6.…

A: Given  a= 2 ,b=6 ,c= 17  x= 1 and y=6 x+iy= 1+6i

Q: (b) Determine whether u(x,t)= e' sinx is a solution to L

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Q: -1 sin t 5 X + 1 X' -1 -2 cos t)

A: Method of Undetermined Coefficient:

Q: Find the general solution of a²z a?z e*-y sin(2x + 3y) + y sin x ax² əy²

A: Given partial differential equation: ∂2z∂x2-∂2z∂y2=ex-ysin2x+3y+ysinx                        . . . .…

Q: Which of the following is a general solution in implicit form? A B C D y=ccosx y=In(cosx+B) + C y =…

A: topic- differential equation Any solution in the form y=y(x) is in explicit form. solution in any…

Q: Determine whether y = e', y, = sin2t, ya= cos2t make up a fundamental set of solutions by finding…

A: The Wronskian matrix is constructed using y1 , y2 , y3 and their derivatives. If the determinant of…

Q: Find the general solution to the given Euler equation. Assume x > 0 9x2y" + 15xy' + y = 0

A: Solution:- The given differential equation is  9x2y''+15xy'+y=0..........(1)

Q: Find T, N, B, K and t for r(t) = (3csc^3t • sin^6t) i + (3sec^3 t • cos^6t)j + 5k

A: given that                                             r→(t)=3csc3tsin6ti^+3sec3tcos6tj^+5k^ now…

Q: Give the Solution of each Non – exact DE. 58) у (8х — 9у)dx + 2x(х — Зу)dy %3D0. The answer should…

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Q: Find the general solution to the given Euler equation. Assume x > 0 x2y" - 5xy' + 8y = 0

A: Consider the following differential equation: x2y''-5xy'+8y=0 Substitute y=xr→y'=rxr-1→y''=rr-1xr-2…

Q: (2)so3ə]E=l2], (22436)9]dz [e cos(z) (z–2)3 Iz|=3

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Q: d^2y/dx^2 + 3dy/dx + 4y = 3x + 2 Utilize the indeterminate coefficient technique to solve the above…

A: Here is the, solution

Q: Find the general solution to the given Euler equation. Assume x > 0 x2y" + 3xy' + 10y = 0

A: Consider the Euler equation x2y''+3xy'+10y=0. Let y=xr Implies y'=rxr-1 and y''=r(r-1)xr-2.…

Q: Find the general solution to the given Euler equation. Assume x > 0 2x2y– + 7xy' + 2y = 0

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Q: Determine whether Y = e', y2 = sin2t, y3 = cos2t make up a fundamental set of solutions by finding…

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Q: Suppose z = x + 2i and u = 3+ yi where x, y E R. Find the smallest positive value of x z + u for…

A: Given that z=x+2i and u=3+yi where x,y∈R. Now our aim is to find the smallest value for x for which…

Q: Which is the solution to the equation 7n 37 2sin22x + 3sin2x + 1 = 0, x = 6

A: 2sin22x+3sin2x+1=0 Put x=7π6 in the given equation, we get…

Q: Evaluate the complex integral e19.2.png x+yi Vaz + b dz 0. if a = 10, b = 19, c = 10, x = 1, and y =…

A: To find- Evaluate the complex integral ∫0x+yiaz + b dz if a = 10, b = 19, c = 10, x = 1, and y = 5.…

Q: Find an explicit general solution for 1) y' 11 + y = +C 2) y' = -5 sin x + 7 cos r → y = +C 3) y' =…

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Q: Q1) Solve the BVP u₁ = Uxx + sin 2x, u(0,t) = 0, u(π, t) = 0 u(x,0) = 0 00

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