Find a differential operator that annihilates the given function 1. y= 4e* +3e¯* 2. y = 2e cos 3.x 3. y = xe sin 2.x +3e cos 2.x

Q: For exact differential equation of the form Mdx + Ndy =0 %3D OA ay %3D В. Эх dy 0: D. ay

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Q: Find the particular solutions of the given differential equation dy dz 2 cos a sin a given y = 1…

A: 1. Sin(2A)=2sin(A)cos(A). 2. Sin²A+Cos²A=1.

Q: Use any appropriate method in finding the indicated solution of the following differential…

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Q: Solve the following differential equation using determination of integrating factors: 2y (x2 - y +…

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Q: Verify that the given function y = sin (x2 + C ) is a solution of the given differential equation:…

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Q: Find the solution of the following Differential Equations 5) sinh(x)cos(y)dx = cosh(x) sin(y)dy 7)…

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Q: Find the value of a and b for which the given differential equation is exact: *siny + (a - 3)ysinx)…

A: Equation is exact for the values a= 5 and b= -1 Therefore option C is correct

Q: 33. Find a linear differential operator (of lowest order) that annihilates the given function: f (x)…

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Q: 2. Show that these differential equations are exact, then integrate to find the solution. (a) dy +y…

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Q: Show that given differential equation is exact and hence solve it (y sin z)dr - (y+y+ cos a) dy = 0,…

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Q: Find all values of k for which the function y = sin(kt) satisfies the differential equation y" + 17y…

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Q: Evaluate the given differential equation (3siny – 5x)dx + 2x°coty dy = 0

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Q: Consider the following differential equation. 2y'' + y' − y = 0 Exercise (a) For what values of…

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Q: (х + 2) dx (x + 3) sin y cos y dy In(x + 3) sin? y + C - ans. 2 2.

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Q: Evaluate the given differential equation cosy sin2x dx + ( cos²y – cos x)dy = 0 A. cos x (1+ siny) =…

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Q: Find the integrating factor so that the given differential equation will become exact DE. – 3) dæ +…

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Q: Find the general solution of the following differential equations. 3. (cos x cos y – cotx)dx – sin x…

A: compare given DE with Mdx + Ndy = 0  and then solve

Q: Find the general solution of the following differential equations using Variable Separable. 1.…

A: We need to solve differential equation by variable separable method.

Q: What is the general solution of of the differential equation y = ysecz ? O (sec z+ tan z) - c O y…

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Q: Consider the following differential equation: (12xy3+32ysen(xy)cos(xy))dx+N(x, y)dy=0 Calculate N…

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Q: Find the differential equation of the following function (х — Зу + 2)dx + 3(х + Зу — 4)dy — 0 х-1 a.…

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Q: The differential equation formed by eliminating arbitrary constants a and b of a sin x + b Y = 9 is…

A: We will differentiate the  y twice to get desired differential equation

Q: x(In y – In x)dy = y(1+ In y - In x)dr

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Q: The non-exact differential...(x² + y²)dx + (3xy2 + 2xy + x³)dy = 0 can be reduced to exact after…

A: We need to determine the integrating factor for the differential equation: x2+y2dx+3xy2+2xy+x3dy=0…

Q: Verify that the indicated expression is an implicit solution of the given differential equation. 1 (…

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Q: Obtain the general solution of the differential equation x²y" = xy' + sin(ln(/T)) for x > 0 It may…

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Q: Determine whether the family of functions x = c, sin t + c2 cos t is a solution of the differential…

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Q: Find the differential equation of the following function (х — у + 2)dx + 3dy —D 0 a. y = x + 5 + Cea…

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Q: verify that the given functions are solutions of the differential equation, and determine their…

A: Differentiate y=1 with respect to x. y'=0 Differentiate y'=0 with respect to x. y''=0 Differentiate…

Q: Find the general solution of the differential equation y" + zy' + 25y = 6 cos(5 In z) + 6 sin(5 In…

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Q: Consider the differential equation y" – 2y'+ 37y = 0; e* cos(6x), e* sin(6x), (-o, ). Verify that…

A: y(x) = ex(C1cos6x +C2 Sin6x)

Q: What is N(x,y) for the following differential equation: x(1 - sin y)y' %3D (сos x - сos y — y)

A: Given a differential equation, x1-sinyy'=cosx-cosy-y

Q: b) Form the differential equation from the function x = Acos(nt + a). e) Given that y = eax sin bx,…

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Q: (ysin x+xy cos x)dx+(xsin x +1)dy = 0 Ans. xy sin x+y = c

A: A differential equation of the form M(x,y)dx+N(x,y)dy=0 is said to be exact iff ∂M∂y=∂N∂x

Q: Which of the following function can be used as an integrating factor for the non-exact differential…

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Q: Solve the following differential equation given the initial value. dy = tan(x), y(0) =1 dx A y = In|…

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Q: Find a differential operator that annihilates the given function. 1. y=4e* + 3e¬* 2x 2. y= 2e* cos…

A: The annihilator approach in differential equation is used to solve a non homogeneous ordinary…

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Q: What are the associated roots forR (x) in the differential equationy''- y = R(x) where R(x) = 4cosx?…

A: Given differential equation:- y"-y = R(x) Where R(x) = 4 cosx

Q: Find the particular integral of the following differential equation d2y/dx2 +9y =cos3x by first…

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Q: Find the particular solution of the given differential equation of order one below, such that when x…

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Q: Verify that the indicated function is an explicit solution of the given differential equation.…

A: Given:     y''-6y'+25y=0     y=e3xcos4x      y'=ddxe3xcos4x  Apply the product rule:…

Q: Find a linear differential operator that annihilates the given function. (Use D for the differential…

A: If a linear differential operator is applied to an expression and the result is 0, then it is called…

Q: 2. (x + 2) dæ: (x + 3) sin y cos y dy In(a + 3) sin y %3D + C ans. x -

A: (x+2) dx = (x+3) sin y cos y dyUsing the method of variable separable;x+2x+3 dx = sin y cos y dy…

Q: dx + 2- + x = u(t) x(0) = x'(0) = 1 dt %3D %3D dt

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Q: How does the following differential equation (y+2xy*) dx + (1+ 3.x²y² + x) dy = 0 satisfy the…

A: When the partial differentiation is done with respect to a specific variable, then all other…