Obtain the general solution of the differential equation x²y" = xy' + sin(ln(/T)) for x > 0 It may be useful to note that: In(z) sen 2 In(z) 2 4 sen 2 + cos 2 dr = +C, con C' e R, 17.12

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Q: 7. х%3D Аy? — In By

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A: 1. y-1=x2ex+c Note:     Multiple questions are given, we are answer with only one question. If you…

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Q: Use the initial condition to find the particular solution of the differential equation. dy = 4xy…

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A: Given Information :  Differential equation : dydx = 2cos2x - sin2x + y22 cosx  y1 = sinx y(0) = -1

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Q: Find the particular solution to the differential equation y' + ytanx = sin2x with the given boundary…

A: Given:         Differential equation y'+ytanx=sin2x            y(0)=1 This is in the form:…

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: What is of the differential equation (3 +y+ 2y sin² æ) dx + (x + 2xy – ysin2x) dy = 0 ? O 2x sin 2x…

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Q: [cos y + 1]dy + [tanx (siny + y)]dx = [sin y cos x + y cos x]°dx gettyimages When:x = 0;y=

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

A: See the attachment

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Q: Consider the differential equation 1 y' = x – 2 with the initial condition y (xo) = = Yo What must…

A: We are given : y'=y-13x-2⇒dydx=y-13x-2⇒dyy-13=dxx-2Now, we will Integrate both…

Q: y = C, x? sin 4x + C2x² Cos 4x

A: The equation is y = C1x2sin4x+C2x2cos4x

Q: 5. The differential equation (3x'e' - 2xx+ (r'e' -sin y ldy = 0 is exact because ON

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Q: Q19// Solve the partial differential equation du = Iny sin-x given that дхду = cosx when y-0 and u=y…

A: Initial value problem are those problem in partial differential equation in which initial condition…

Q: 1. x In x sec² y dy + [tan y – (In x)°]dx = 0 When:x = 1; y = "

A: The given differential equation is solved below in detail.

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Q: Find the general solution of the differential equation = 6 tan(5y) using separation of variables. dx…

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Q: The integrating factor of the linear first order differential equation dy dx sin2x- y+tanx Oa None…

A: The standard formula for the linear differential equation is dydx+P(x)y=Q(x). Here, P(x), Q(x) are…

Q: 1. What is the integrating factor of the differential equation ydx – xdy = 0 using case 1?

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

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

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Q: -) Solve the following partial differential equation us ing direct integration: a²u = cos (x +y) дх…

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Q: Show that f(x, y) = e2x cos(x + In y) satisfies the differential equation 2f - yfyx = 5f.

A: Given that fx,y=e2xcosx+lnyShow that 2fx-yfyx=5f

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A: Given that obtain the differential equation associated with the given non-derivative equation in x…

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

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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: Find a particular solution Y of the nonhomogeneous differential equation y'' + y' + y = 2 cost −…

A: Given a nonhomogenous differential equation y''+y'+y=2cost-sint

Q: 3. (cosy + ycosx)dx + (sinx – xsiny)dy = 0

A: Given: cosy +ycosxdx +sinx-xsinydy =0 ⇒cosydx +ycosxdx +sinxdy-xsinydy =0

Q: 1. x In x sec² y dy + [tan y – (In x)°]dx = 0 When:x = 1; y =

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

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Q: 3. (sin'x + cosv)dx - tanxsin2ydy = 0

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Q: Is the differential equation y sin 4x dx + x cos 9y dy = 0 exact? %3D Choose the most appropriate…

A: A Diffrentaial equation in the form :-  M( x, y)dx + N(x, y) dy = 0 is an exact  if,   ∂M/∂y =…

Q: Obtain the Differential Equation from the given general solution. y = C¡ cos(4x) + Cz sin(4x) + Cx…

A: Use the following formula, to find the solution. ddxcosax=-asinaxddxsinax=acosaxddxuv=udvdx+vdudx