Show that an implicit solution of 2x sin?(y) dx – (x² + 16) cos(y) dy = 0 is given by In(x? + 16) + csc(y) = C. = 0 or 2x sin?(y) dx + dy dx 2x 0. + Differentiating In(x² + 16) + csc(y) = C we get %3D x2 + 16 Find the constant solutions, if any, that were lost in the solution of the differential equation. (Let k represent an arbitrary integer.) y =

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A: Given d2ydx2+y=8cos2x-4sinx with yπ2=-1,  y1π2=0

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A: y = 1/4 [ x - 1/2 sin2x] +x -π/4

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A: Obtain general solution  y¹ = cos²x cos y

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A: Please see the explanation below

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A: How can I find the particular solution of y''+36y=cos(6x)

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A:

Q: 6 Evaluate (a) [ a + (4x-2° dx + (4x-2)* dx (2x-3)2 2x sin (x²+!) cos (x+1) dx

A: AS mentioned by you that "none of these is graded please answer 5. These are practice questions"…

Q: Show that an implicit solution of 2x sin?(y) dx – (x² + 17) cos(y) dy = 0 is given by In(x2 + 17) +…

A: To find- Show that an implicit solution of 2x sin2y dx - x2 + 17 cosy dy = 0 is given by lnx2 + 17 +…

Q: (b) Find the solution for cos(x) − (1 + x²) x − 2xy = - - with the conditions y(1) = -1, y(2) = 2…

A: Note:-  For this problem if you want general solution for this problem then please resubmit problem…

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A:

Q: Find the general solution of y'+9 y = 4 cos 2x A. y -A cos 3x +B sin 3x + cos 2r B. y -A cos2x + B…

A: Given information: y'' +9y=4cos2x The second order non homogenous differential equation has solution…

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Q: What is a suitable integrating factor that can be used to solve the equation: X +2у — 4ху - е *cos…

A: topic - integrating factor for differential equation

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Q: Find the solution of the given initial value problem in explicit form. π ㅠ sin (2x) dx + cos(7y) dy…

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Q: Solve the initial value problem.

A: To solve the initial value problem.

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A: Given: cos(x)dydx+y sin(x)=2x cos2(x)

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A: Thanks for the question :)And your upvote will be really appreciable ;)

Q: Find the solution of the given initial value problem in explicit form. 75 π sin (2x) dx + cos (7y)…

A: The given initial value problem is                        sin2xdx+cos7ydy=0,  yπ2=π7 We have to find…

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A:

Q: Find the general solution of y +9y-4 cos 2r A. y -A cos 3x +B sin 3x +c cos 2r B. y -A cos2xr + B…

A: Given: y''+9y=4cos2x

Q: Solve (5x2y2 O a. b. 2 ln 3 In a In xy² + 17y²) dx (x+2)³(x²+9) y³ |(x+2)³(x²+9) Y - -1 3 tan-¹() =…

A: Given 5x2y2-xy2+17y2dx-x3y+2x2y+9xy+18ydy=0

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A: The solution is given as

Q: Show that an implicit solution of 2x sin?(y) dx - (x2 + 17) cos(y) dy = 0 is given by In(x? + 17) +…

A:

Q: Find the solution of the given initial value problem in explicit form. ㅠ sin (2x) dx + cos(7y) dy =…

A: Here we use basic integral to find the solution.

Q: What is the general solution to the differential equation (tan x)dy – (4yIn y – y tan³x)sec?x dx = 0…

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Q: Find the solution to the initial-value problem. dy dx = y2ex sin(7x), y(0) = 1 y

A: We will solve the given differential equation as shown below