Obtain the general solution unless otherwise instructed a.) (9D4 + 6D3 + D2)y = 0 b.) (4D4 − 45D2 − 70D − 24)y = 0 c.) [(d3x/dt3) − 2(d2x/dt2) − 3(dx/dt)= 0

Q: nd the general Solution of the tfferential equation. (x+2y-1)dx+(3x (3x+by)dy = C

A: The differential equation is given as , x+2y-1dx+3x+6ydy=0. Simplify the differential equation,…

Q: The solution of: v(t) = e =t + ] sin(t - T)y(T)dt , in terms of convolution is:

A: Convolution theorem of Laplace transform    Laplace transforms of the functions Inverse Laplace…

Q: Solve the Cauchy euler equation d³y x3 dx3 3x2 d?y dx2 2 + 6x -6y = 3 + Inx³ dy dx

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Q: Exercise 3. compare the values of dy and Ay in each case (3a) y = 0.5r" I = 2 Ar = dr = 0.1 (3b) y =…

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Q: d²y - y = у 3 10sin?x %3| dx2

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Q: Find the general solution of (D4+ 50D²+625) y=0_ A y=c,cos5x +c,sin5x ® y=c,e*+c,x* +cze-5«.…

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Q: Find the solution of the second order homogeneous linear equation when d2y/dx2-4 dy/dx - 4y = y ; y…

A: Given differential equation is d2y/dx2-4 dy/dx - 4y = y ; y (0)=1 ,y'(0)=2

Q: dx -2xcsc 2y – 2x³cos 2y dy sec 2y

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Q: Find the general solution of using the method of variation of parameters. d²y dy 2- - 42+ 2y = xe 2x…

A: Given,2y"-4y'+2y=xe2xComplementary SolutionAuxiliary Equation is 2m2-4m+2=0⇒m2-2m+1=0⇒m-12=0⇒m= 1 ,…

Q: The general solution to d?y/dt2 = 25y is

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Q: В. NON-HOMOGENEOUS HIGHER ORDERED LDE 1. (D3 + 5D² + 3D - 9)y = 64x²e-3x 2. (D³ + 13D - 34)y = 25x2…

A: As per our guidelines, we are supposed to solve only first question. Kindly repost other question as…

Q: Solve the DE by Variation of Parameters (D³ + D² – 2D) y = 4e 2" cos a Cos r y (0) = 0.4, y' (0) =…

A: given (D3 + D2 − 2D)y = 4e−2x cosx The auxillary equation is m3 + m2 – 2m= 0 m(m2  + 2m - 2)=0…

Q: Given that d²y 2. +y =0. dx2 Show that y = x is not Solution a

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Q: Consider the DE d?y dy + - 6y = 12x, y(0) = 1 - dx? dx 1 is a solution of the DE and determine 3…

A: y=Ae2x-2x-13 Differentiating with respect to x, we get dydx=A·2e2x-21-0   ∵deaxdx=aeax, dxndx=nxn-1…

Q: B. In each exercise, obtain the particular of solution. 2. y(9x - 2y) dx - x(6x – y) dy = 0; when x…

A: Differential equations

Q: Solve the I.V.P: dy = 6y²x; y(1) = 6y?r; %3D dx Oy 1 372-8 1 Oy = 8-3z2 Oy 1 8+3z? Oy = 1 !! 8-3z

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Q: Find the complete solution of the DE (D3+6D2+11D+6)y=ex +cosx.

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Q: 1. (3x – 2y + 1) dx + (3x- 2y +3) dy = 0, %3D Ans. 5(x + y+ c) = 2 In | 15x - 10y + 11L

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Q: In each exercise, obtain the particular of solution. a. xy dx + 2(r? + 2y?) dy = 0; when x 0, y = 1

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Q: Find the solution. d3x d?x dx – 2–=0 dt + dt3 di2 -21 ® y = c,+c,e'+c,e- -31 D y = c,++ce+c,e-2

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Q: Find the Particular solution of the ODE d?y dy -6--7y = -9e-2x, dx2 at y(0) = -2 and y(0) = -13 %3D…

A: We have to find the particular solution of the ODE                       d2ydx2-6dydx-7y=-9e-2x at…

Q: Find the solution. (D4 + 18D2 + 81)y = 0 A y = (c, + c,x)e²"cos3x + (c,+cx)e2'sin3x. y = (c, + c,)…

A: 16 Given differential equation is D4+18D2+81y=0 We have to find the general solution of the given…

Q: dy Find a solution of x dx = y². - y that passes through the indicated points. (a) (0, 1) y = (b)…

A: First we'll solve differential equation then put intial conditions

Q: Determine the solution y(t) of the IVP then find y'(t). 2y'' + 3y' − 2y = e4t cosh3t,        y(0) =…

A: Ordinary differential equation involves derivative with respect to one variable.

Q: 5. dy 4y-3x 2x-y dx

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Q: dy Find a solution of x dx y2 - y that passes through the indicated points. (a) (0, 1) y = | 0

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Q: SI, (x2 + y2 + z²) dxdydz , where T: 0<x < v4 – x², 0 < y < 2, /x² + y² < z< J4 – x² – y2

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Q: Find the particular solution of the DE x?dx +ydy =0, when x = 2, y 1. O 2x3 + 3y2 = 19 O 2y + 3x2 =…

A: Given, differential equation,x2dx + ydy = 0Integrating on both sides, we get∫x2dx + ∫ydy = Cx33 +…

Q: What is the general solution of the given DE m2y = C,e™1* where C1, m1, m2 are constants dx and m, +…

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Q: dy 1. dr + 3y = 2xe -3z %3D

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

Q: c) Show that y(x) = 1+ax+bx², where a and b are non-zero, is a solution to Laguerre's equation, d²y…

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Q: (2, 3), dy If x2 + xy = # = 10, then at the point dx

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Q: Solve the DE by Variation of Parameters (D³ + D° = 2D) y = 4e¯= cos z -2x COs I y (0) = 0.4, y' (0)…

A: The differential equation is D3+D2-2Dy=4e-2xcos x with the initial condition y0=0.4, y'0=-0.4,…

Q: 3. Find the general solutions of, dy _ x+ y dx х-у, a.

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Q: 2. In each exercise, obtain the particular of solution. 2y-) dy = 0: when x= 0, y = 1 (3x +v) dy =…

A: As per Bartleby guidelines for more than one question asked only one is to be answered please upload…

Q: dy - Find the general solution of Y +2 = 3x²y² dx A. 1/(xy) = -3(x³/2) + C B. 1/(xy) = -3(x²/2) + C…

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Q: Solve the system of equations below dx = 5x – 3y dt dy 11x – 9y dt %3D

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Q: 6. dy dx 4x + 3y 2x+y

A: Solution :-

Q: ds Differentiate with respect to t and solve for dt s2 = x² + y? %3D 2s ds dt = 2x + 2y dt dt x + ds…

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Q: Fınd the general solution of x²5 d²y + 2x- 2y = 0 dx² dy dx where y(x) = x is a solution.

A: c1 and c2 are arbitrary constant.

Q: 2. Solve (y 2)dx (x- y 1)dy 0 using the method for linear coefficients in two linear variables. %3D…

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Q: If y(t) is the solution of - 2y = 4, y(0) =1, then y(t)= %3D %3D

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Q: Consider the DE d²y dy dx? 6y = 12x, y(0) = 1 dx 1 is a solution of the DE and determine 3 Verify…

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Q: dy Obtain the general solution to the equation + 2 = xy² а. ху(-x + C) %3D 1 b. ху(x + C) %3D 1 dx…

A: This question is related to differential equations, we will solve it using given information.

Q: u2-1 Given y = dy and u = Vx2 + 2, find dx %3D u3+1

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Q: Solve the equation, d²x + w?x(t) = 0 dt? subject to the conditions x(0) = A and x'(0) = 0 %3D %3D

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Q: 3. dy dx x² + xy + y² x²

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Q: Find the solution. (D4 + 18D² + 81)y = 0 A y = (c, + cx)e²"cos3x + (c,+cx)e²"sin3x. B y = (c, + cz*)…

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Q: Fınd the general solution of d²y dy + 2x - 2y = 0 dx dx² where y(x) = x is a solution.

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Q: Q6: Solve the following Higher-Order D.E. d³y d²y dy + 7- 5y = 0 dx 3 %3D - dx3 dx2 To find the…

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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.