Find the particular integral of the following differential equation d2y/dx2 +9y =cos3x by first substituting cosαx with e^iαx then use the shift operator and finally extract the real part .Therefore prove that the answer is  1/36(6xsin3x+cos3x)

Q: The complementary function(C.F.) of the differential equation (D – 7)(D² + 7?)y = e7² is O (c2 Cos…

A: Solution: The objective is to find the complementary function of the given differential equation

Q: Determine the following differential equation by appling the Leibniz-MacLaurin method…

A: Given the differential equation:  Differentiate both sides with respect to x , upto n times by using…

Q: The complementary function(C.F.) of the differential equation(D – 8)°y = sin 8x is (ci + c2x +…

A: Solution: The objective is to find the complementary function of the given differential equation

Q: y = (C₁ + C₂x) eª + sinx+x²; y" - 2y' + y = −2 cos x + x² − 4x + 2

A: Here we find the first and second derivatives of given solution and then put in the left hand side…

Q: Solve. dy 2у %3D 10х3. dx

A: As per our guideline we are supposed to answer only first asked  question. Kindly repost other…

Q: c. y" +4y=tan2x %3D

A: Solution of the given differntial equation is

Q: Identify which below is a separable Ordinary Differential Equation 2xy a. y': х(у — 1) — у dy _x+ y…

A:

Q: Since dv = cos( cos9 x) dx, integrate the differential equation to obtain the function v. V = ^p -…

A: We have to find solution

Q: The complementary function(C.F.) of the differential equation (D² + 6D+18)y=x is_ -37 (c1 cos 3x +…

A:

Q: The complementary function(C.F.) of the differential equation (D2 + 6D+ 18)y= z is_

A: In this question, we have find the complementary function for the differential equation.

Q: Use the inverse differential operators to solve the initial value problem: 2y'' + 5y' + 2y = e2x

A:

Q: The following ordinary differential equation is given: dw /dx + 1.1w = wx^2 with w(0) = 1. Use…

A:

Q: Solve the following separable differential equation; write the general solution explicitly as a…

A:

Q: transcribe the following text in digital format

A: In the question, it is asked to transcribe the given text in the screenshot to digital format.…

Q: Solve the differential equation by using variation of parameters: d'y dy 3 dx 3x + 2y = e dx .A 3x y…

A:

Q: <ソ+メ-3) (メ-344)ゾ ニ t.

A:

Q: Can you provide 1 example of Differential Operators (4th order 1 Imaginary and 1 Repeated Distinct…

A:

Q: Evaluate the given differential equation y' tan x sin 2y = sin*x + cos?y A. sinx (sin?x + cosx) = C…

A: Explained below

Q: Solve the following differential equation y'"+2y' +5y= e2*coshx Select one: O a.…

A:

Q: Let c be a real number. By taking the necessary derivatives, show that the function f(x,t)= ln(x+ct)…

A: The given function is

Q: The table below gives values of the function f (x, y), which is increasing in xand decreasing in y…

A: Given, o≤x≤6,   0≤y≤1 ∆x=6-02=62=3∆y=1-02=12=0.5 From the given data. f0,0=4       f3,0=7…

Q: Find a differential operator that annihilates 4e2" cos 3x + 3x²e5.

A: Let L be the differential differential operator that annihilates 4e2xcos3x+3x2e5x. Find L.

Q: Form the differential equation for the function 2xy= asin2x -bcos2x O a. xy" +2y' = – 4xy O b. xy"…

A:

Q: 12 Use differentials to calculate solution. √102. Show comp

A:

Q: Find a linear differential operator that annihilates the function 2x + 4xex D'(D - 6 D(D - 6) D'(D -…

A:

Q: у" + 16у — 0; Уi — сos 4x

A:

Q: 2y' =√x + 2y + 1|

A: Given differential equation is By substituting [ differentiating both side with respect to x ]Thus…

Q: LINEAR DIFFERENTIAL OPERATOR N FUNS TIO

A:

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.