Which one of the following is a 3rd order Ordinary Differential Equation, (dy dy =D0 dx du a'u 3D0 ду None of These dx' dx

Q: (3ху2 — у?)dx + (2х?у - 2у)dy - 0

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Q: Which of the following is the Euler (Cauchy) differential equation whose general solution is y =…

A: In this question, the general solution of the Cauchy  equation y=c1cos(lnx)+c2sin(lnx) It is…

Q: Form the differential equation by eliminating the constant 'a' from r=2a (sin 0- cos 0)

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Q: Write down a differential equation of the form dt all other solutions diverge from y = 4 as t →∞.…

A: Let us consider a differential equation dydt=ay+b  such that the solution diverges as t→∞, y=C The…

Q: The particular solution to the nonhomogeneous differential equation y" + 4y' +5y = 10x + 3e-* %3D

A: The given differential equation y''+4y'+5=10x+3e-x. The particular integral is computed as follows,…

Q: What is the solution to the differential equation 2 = 2xy satisfying the boundry condition y = e…

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Q: b Show that y = e' sinx %3D satisfies the differential equation (1 - x²)y" – xy' - y = 0. |

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Q: ( .) Find the solution to the differential equation dz dt that passes through the origin. 2= 5te6z

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Q: Form the differential equation whose primitive is given by y= ex(a cos⁡x + b sin⁡x),  a, b, being…

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Q: Obtain the differential equation by eliminating a and b from the rdation y=a cos 4x +b sin 4x

A: Given equation is y=a cos4x + b sin4x find out the DE by eliminating a and b

Q: x³y"+xy'+4y = cos (2 ln x) bulunuz.

A: See the attachment

Q: Suppose that x = 0 is a regular singular point of the differential equation 4xy" + 2y' + y = 0 Then,…

A: Given: x=0 is a regular singular point of differential equation 4xy''+2y'+y=0. To find: Indicial…

Q: Form a differential equation from the given function. y = Asin(2x)-5cos(2x)

A: Giveny=Asin(2x)-5cos(2x)   ----{1}

Q: What is the particular solution to the 2² +3 with the differential equation dy da 3y initial…

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Q: Which of the following is a nonhomogeneous linear differential equation with constant coefficients?

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Q: Q1 By eliminating the constants A and B from the equation y = Asin 2x + B cos2x, form an ordinary…

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Q: Use separation of variables to find the general solution of the differential equation. 6 cos(tx) xp

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Q: The standard form of the differential equation cosx y' + cosx y = x sin x is: None of the above O…

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Q: y= 4 + Inx; xy'

A: Since you have posted multiple questions i can do first question as per our company guidelines…

Q: State where in the ty-plane the hypothesis of the (non-linear) Existence and Uniqeness Theorem is…

A: Given: The given differential equation is y'=t-y2t+5y

Q: 2. y" + 25y = 5 tan² (5x) cos(5x)

A: The given problem is to solve the given differential equation, we have to solve it by using…

Q: -ka dt2 Sdlve the differential equation and express the X func tion of trieonometrie func tion as

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Q: What is the auxiliary equation associated with the second order linear differential equationd^2x…

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Q: 5. In the differential equation (1+3xsin ykdx-x cos ydy = 0, we let the substitution %3D

A: Follow the procedure given below.

Q: THE

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Q: FIND THE GIVEN DIFFERENTIAL EQUATION Non Exact Eguation (xy + 1) dx tx (* + 4y - 2) dy - 0

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Q: y" + 25y = 5 tan²(5x) cos(5x)

A: To Determine :-  The second order differential equation : y'' + 25y = 5 tan2  5x cos  5x

Q: Consider the differential equation curve if it passes through (1,-1). dy 2y dx x = 0. Find the…

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Q: d²x 7x + 3- dt2 dt 2- - t dx

A: 7x+3d2xdt2=2dtdx-t Multiplying both sides by dxdt , we get 7xdxdt+3d2xdt2dxdt=2-tdxdt              1

Q: - ydx + (x ++ Vxy )dy= 0

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Q: Q-2. Form the first-order differential equation of ey = sinx

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Q: 3. Show that the differential equation zxy

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Q: Find the differential equation by eliminating the arbitrary constant/s. 1. ecosx = c(1-cosy)-¹

A: Since you have asked multiple questions in a single request we would be answering only the first…

Q: The degree and order of the differential equation 1+ is = dy dz о 12, 1 O 1, 15 O 15, 1 O 3, 1

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Q: Solve the 2nd order linear differential equation y" – y' = 5e* – sin2x %3D

A: The auxiallary equation for the given differential equation is given by

Q: Write down a linear homogenous differential equation (with the smallest order and constant…

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Q: а. у %3D Ае2х + Вхе2x

A: We eliminate A and B by taking first derivative y' and second derivative y''

Q: Solve the given differential equation by separation of variables. y In(x) *- (1)* %3D Ap

A: Solution :-

Q: The point Xg-0 is a singular point to the differential equation csc(x) y" +-y-y-D0. Select one: O…

A: Given differential equation is cscxy''+1xy'−y=0.....1. We have to check whether the point x0=0 is a…

Q: 9. The differential equation (3y cosx+4xe" + 2x'e' dx + 3(sin x +1)dy=0 is exact because aN

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Q: What differential equation has y = x² cos y - 4x + C as a solution?

A: We have to find

Q: 4te dt TOT

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Q: The roots of an auxiliary equation are m1=4, m2=m3=-5. What is the corresponding differential…

A: If the root of the auxiliary equation is m1=α and m2=β, then the corresponding differential equation…

Q: a) Predict if the following differential equation is exact or not. Hence solve it. dy xy-cos xsin x…

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Q: Which of the following can NOT be the linearly independent solutions of the differential equation y"…

A: Here 1, x are the solutions of ode. then their linear combinations also solution  but option C can’t…

Q: (x-C,)' +y° = C;?

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Q: 5. In the differential equation (1+3xsin y dx– x² cos ydy = 0, we let the substitution %3D

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Q: Solve the Cauchy-Euler differential equation on the interval (0, ∞). ry" +6x²y" + 4xy' - 4y = 0

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Q: y'tanxsin2y = sin²x + cos²y

A: Assume t=cos2y then differentiate both side with respect to x to find dtdx .…

Q: Show that y1 =- and y2 = Vx are solutions of the following differential equation 4x3у" + 7x?у' — ху…

A: According to the given information, it is required to show that the given y1 and y2 are the…