For the equation e - z = 2014 in the left half-plane {z € C: Re (2) < 0} show that: (a) there exists exactly one solution, (b) the solution is real.

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A: Result used:

Q: When reduced to a linear DE of order one in z, the Bernoulli's equation +y()= 3x?y² becomes +z(-÷) =…

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Q: ) y, = x2 IS ODE X²y"+2y-6y=0 SOLUTION OF THE USE THE REDUCTION OF ORDER FOAMULA TO FIND A SCCOND…

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Q: Determine the largest interval (a,b) for which Theorem 1 guarantees the existence of a unique…

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Q: EXERCISE 1. dy ry+y Find the general solution of dr

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Q: Q8. Solve the non-homogeneous Cauchy-Euler equation (a) x?y" – 2y = 3x².

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Q: Show that if n ≠ 0, 1, then the substitution v = y1 − n reduces Bernoulli’s equation to a linear…

A: Given: n≠0,1y'+p(t)y=q(t)yn

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Q: Suppose that f(t) = e (1−2i)t is a complex solution for an unknown second-order linear equation…

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Q: (B) Find the solution of f(z) = x'+6x°y+i 3x'y by using Cauchy-Riemann method %3D

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Q: Show that y1(t) = et and y2(t) = e−3t form a fundamental set of solutions for y'' +2y' −3y = 0, then…

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A: Let's find.

Q: (1) こ Wy2,y2)= 12 enx (2) 9/2 X 9) Y=(x)=e

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A: By finding the wronskian of the solutions

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Q: Prove that if y1 and y2 are linearly independent solutions to thehomogeneous, then the functions y3…

A: Given:y3=y1+y2y4=y1-y2

Q: Determine the largest interval (a,b) for which Theorem 1 guarantees the existence of a unique…

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Q: eメ B-4D+

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Q: Determine the largest interval (a,b) for which Theorem 1 guarantees the existence of a unique…

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Q: Consider the following where c,, c2, C3 and ca are constants. c,(1 - 4x) + c2(9x + x2 - x) + c3(1 +…

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Q: Solve the Cauchy-Euler equation: x*y' Зху + 4y = 0. %3D

A: Given Cauchy-Euler differential equation is

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Q: 7. State whether the equation is ordinary or partial, linear or nonlinear, and give its order. * ()…

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Q: Exercise 2 Eliminate the arbitrary constants of the following. General solution 1. y = cx + c + 1

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Q: Determine a general solution to the Cauchy-Euler equation z'y"(x) – 2y(z) = 3z² – 1, z>0.

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Q: x²y" – 4xy'+6y= 0, y(2)= 0, y'(2)= 4 %3D -

A: Given differential equation is: x2y''-4xy'+6y=0           y(2)=0; y'(2)=4 In Cauchy Euler method we…

Q: (g) Any separable equation M(x)+N(y)y' = 0 is also exact. %3D

A: Since you have asked multiple question, we will solve first one for you. If you want other question…

Q: When reduced to a linear DE of order one in z, the Bernoulli's equation +y(-)= 3x²y² becomes A none…

A: We have to write the differential equation in terms of dz/dx.

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Q: A second order Caushy - Euler equation having a solution y(x) = x=²cos(3Inx) is Ox²y" +5xy' + 4y = 0…

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