Q1/ Study the Cauchy -Riemann equations and determine this equation satisfy it or not. f(z) = e' = e*(cos y + isin y)

Q: Consider the second order differential equation Find all singular points and classify them. y" (x) +…

A: A singular point is point when the point is not ordinary point .

Q: Q.2) The basts of the equatioon y'' + y" = 0,are: b) 1,1.e a) 1,1.e c) 1, x,e²* d) 1,x.e" 0 about

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Q: All numerical angles(phases) should be given in radian angles (not degrees). Given the differential…

A: Given - All numerical angles(phases) should be given in radian angles (not degrees). Given the…

Q: a) f(z) = 2x + ixy2 b) f(z) = x² +iy2 %3D c) f(z) = e*e¯y

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Q: a) m - 1 b) m – 2 Q.8) The characteristic equation for y"" + 3y" – 4y = 0 , is : b) 2' = 32?-4 c) m…

A: To find out the characteristic equation.

Q: Find the solution. (D3 +7D2 + 19D + 13)y =0; when x =0, y=0, y' =2, y"=-12 (A y = e*cosx B y =…

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Q: the derivatives of y with respect to x: y = xe* – ex y = e(1x+) %3D y = e*(sin x + cos x) %3D y =…

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Q: Q.4) The Wronskian W(e~2", e",e²), is: a) 12e b) –12e c) 6e² d) -6e"

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Q: Euler Equation: t2y''+ty'+y=0, t>0

A: Here I am attaching image so that you understand each and every step.

Q: Solve Q11

A: 11. Given that the series                      x∑m=1∞mamxm-1+∑m=0∞amxm

Q: a) 12 Q.7) To write the power series £=3 4m as the form -4m a) m - 1 we must shift m to become : d)…

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Q: DON'T USE CHATGPT Solve the following equation by canceling operator y"+y = 3x sin(x) (In the answer…

A: First of all we find the auxiliary equation for the corresponding homogenous equation. Find the…

Q: 3. (a) Show that (z²z) does not exist anywhere. (b) Verify Cauchy-Riemann equations for the…

A: Cauchy Riemann equation: Let us consider the function f(x+iy)=u(x,y)+i v(x,y)  then the C-R…

Q: 3. Find all solutions of the DE y"-12 y'+36 y=16 te (where t is a real constant) 6 x

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Q: Hint: Use method of undetermined coefficient Solve using the differential operator D=d/dx y" - 2y' +…

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Q: Q.12) The solution of y" + y' = 0 by using power series method , is! %3! a) y(x) = a, – a,(1-+ b)…

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Q: Q.1) The general solution of the equation e' cos , is:

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Q: Show that a harmonic function u (x, y) satisfies the formal differential equa- = 0. azdz

A: Consider the provided question, Given, ux,y is harmonic function. We have to show that ∂2u∂z∂z¯=0.…

Q: Q1) Find the exact sol of differential equation xy'+ y 2x, y(1) = 2

A: Given differential equation is xy'+y=2x, y(1)=2 To find the exact solution of the differential…

Q: Solve

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Q: Classify and reduce the following equations into canonical form : (a): e"u +e'uy =u. (b): x²u +…

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Q: Obtain the roots and the factored operator form linear differential equations y = x2 – 5 sin 3x

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Q: dy' dx (6.) (i + cos x ) = X = 0 y = 1 sinx (sinx tsinxcosx -y) Answer: C=1/12/2

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Q: The direction field for dy/dx = 2x+y is shown in Figure 1 13

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Q: QI/ Study the Cauchy -Riemann equations and determine this equation satisfy it or not. f(z) = e =…

A: Given that: f(z)=ez=ex[cosy+isiny]

Q: c) y(x) = c, + cz + Acos3x + Bsin3x Q.6) The singular point (s) of (x² + 4)y" – x y' + 4y = 0 , is…

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Q: (b). Find a general solution to the given Cauchy-Euler equation for t > 0. t²y" - 3ty' + 3y =…

A: To Find: A general solution to the given Cauchy-Euler equation for…

Q: Write the given second order equation as its equivalent system of first order equations. u" + 4.5u'…

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Q: Find y as a function of t if 7y" + 28y = 0, y(0) = 4, y'(0) = 3. y(t) Note: This particular weBWork…

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Q: Q.1) The general solution of the equation y e' cosA a) y(t) =c, +c; x +c,¢ ' de' cosa Re' sinx b) y…

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