23. Is either of the following equations correct? Give reasons for your answers. + c i dx = x In |x| + Cb. x/ dx = x In |x| + Cx а. х

Q: Find the general solution of the equation x(y2 + 1)dx + (1+ x²)dy = 0. A. In(x2 + 1) + 2Arctan y = c…

A: The given equation is; x(y2+1)dx + (1+x2)dy =0

Q: 3. (x² + 6y²)dx – 4xydy = 0 , y(2) = 1

A: Problem is in the form of homogeneous form...so put y=v.x and proceed as I have done solution step…

Q: III. Determine the solutions of the following DE. 1. xy dx + (y + 1) e¯*dy = 0 2. (2xy – y)dx + (x?…

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Q: Which of the following is the particular solution to the DE y(9x – 2y)dx – x(6x – y)dy = 0; y(1) =…

A: Given differential equation is y9x-2ydx-x6x-ydy=0 and y1=1 Given differential can be written as:…

Q: 5. Find the general solution of the given DE: 2x + 2xy2 y + 2x?y dy dx

A: First We will separate X and y terms of the given differential equation and than integration gives…

Q: Solve the particular solution of the given DE: x(r^3-xy^2+2y^3 )dy-y(r^3+2y^3 )dx=D0 @r=1, y=1.

A: We have to solve given problem:

Q: Find the particular solutions of the following separable equations. 4 — 2х dy dx Зу? - 5' *+1 = 2y –…

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Q: A particular solution of 4x' d´y dx? +8.x- dy 4 is +y de

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Q: SIder ne DE dy dy 6y = 12x, y(0) = 1 dx dx? Ae2 1 is a solution of the DE and determine Verify that…

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Q: Solve for the general solution of the given non-exact DE. y(2x + y?)dx + x(y² – x)dy = 0

A: The given differential equation:y2x+y2dx + xy2-xdy=0We need to solve the above equation.

Q: Evaluate the following problems by obtaining the general solution. Show complete solution.…

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Q: (у — ӕ + хусotx)dx + zdy — 0 y(0)= 3

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Q: Solve the following Initial value problem: xcos²(y)dx + tan y dy = 0, y(a) = b %3D

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Q: Find the general solution of the given Attached equation

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Q: If yo is the particular solution of dy 4x y, y(0) = 3, dx find the value of yo(2).

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Q: 4- Solution of the following equation 4xy?dx + (x² + 1)dy = 0 is O (x+1)/y In( x+1)/y O None of the…

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Q: 1. Find the family of solutions to the following DEs. y' = e"-y + x?e-y dy + y? = 0 dx V1+ a² y/ 1+…

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Q: (a)Use the shooting method to solve: d'y dy = e*; y(0) =1; y(1) =-1. dx dx? Use h=0.1

A: Given that, d2ydx2-ydydx=ex; y(0)=1, y(1)=-1h=0.1 Here we use the Euler's formula: yn+1=yn+hf'xn,yn…

Q: (x² + 6y²)dx – 4xydy = 0,x = 1, y = 1 -

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Q: Solve the first order inhomogeneous equation dy + 2y = 3x2 dx Hint:

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Q: B) Find the general solution to the following DE. dy y? + x2 = 0 dx

A: Given differential equation is y2+x2 dydx=0

Q: dx x- y- dy dx (Separation of variable) dy

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Q: Show that if you differentiate both sides of x 2 + 2y 3 = 6, the result is 2x + 6y2 (dy/dx)= 0. Then…

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Q: Evaluate xy z? dx dy dz

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Q: Find the general solution to each of the following DEs, showing work- ing dy (a) -x = xe dx dy (b) =…

A: (a) Given differential equation is dydx=xe-x Given differential equation can be written dy=xe-x dx…

Q: Find the particular solution to DE:   ( y + square root of x^2 + ?^2 ) dx - xdy = 0 ; y ( √3 ) = 1

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Q: dy Consider the IVP dx (2y – 3x)?, y(0) = 0.

A: Consider u as 2y-3x. Differentiate both sides of the equation u=2y-3x to obtain the expression of…

Q: Determine the solution to this DE: * dy t 3y 2 2 dx

A: an integrating factor is a function that is chosen to facilitate the solving of a given equation…

Q: What is the general solution to the following equation: (dx/dy)+ xtan(y)=2tan(y)

A: rewrite the given equation in the form of separable differential equation and integrate…

Q: Obtain the general solution to the equation. dy y + 2x + 1 dx X The general solution is y(x)=,…

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Q: dy d²y — 4х — + бу 3D 4х — 3 dx² dx

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Q: hat is the answer for this DE? 1.) (2x - y) dx + (4x + y - 6) dy = 0

A: We need to find the solution of the DE(2x - y) dx + (4x + y - 6) dy = 0

Q: I. Find the general solution of the following: 2x* 1. dx 2.d = xy 3. dy = (6e³x + 1)dx

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Q: - For the following, let y(x) Aet? 3 - where A is an arbitrary constant. a. Verify that this y is a…

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Q: 12. Solve the following first-order equations: dy а. = 4x/y, with y(0) = 1 %3D dx

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Q: (4x'y – 15x? – y )dx +(x* +3y² – x)dy=0

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Q: If we solve the DE y dx + 2 x dy 0 alter converting it to Exad using an

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Q: III. Find the particular solution of each of the following. dx 1. dy 2x - 7y*; when y=1,x=-1

A: Find the particular solution of each of the following. dxdy+2xy=7y4; when y=1, x=-1

Q: Show if the following statement is true or false. If it is true, write TRUE. If it is false, write…

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Q: Obtain the general solution unless otherwise instructed 1. arž -y = 10sin²x dx² SUMMARY OF ANSWERS…

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Q: 1. Solve the DE as follows: " +3 d'y dy -+2y= 24 y(0) =10 and y'(0) = 0 di? dt

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Q: 1 If y = tanu, u=v--, and v= lnx, dy at x=e? dx what is the value of Select one: a. 0 O b. 1 1 C. d.…

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Q: 2xdy + y(2 + xy²)dx = 0 %3D 1 when x = 1 & y= 2

A: Given equation is 2xdy+y(2+xy2)dx=0 and y(1)=1/2

Q: Find the complete solution of the following higher order D.E. d3y 4. dx dy? + 6 17 dx2 dy + 92 y…

A: The given differential equation is; 4d3y/dx3 + 6d2y/dx2 -17dy/dx + 92y = 4-4x2+sinx.

Q: 2 dy = Y – xy; y (–1) = 1 dx

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Q: II. Solve the following first order DE. (x² + y²)dx + xy dy = 0 4.

A: Explanation of the solution is given below...

Q: What is the value of the arbitrary constant of the given DE (3x + 2y + 7)dx + (2x – y)dy = 0 at…

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Q: Find the solution of the following: 2. e2x (2cosy dx - sinydy) = 0; y(0) = 0 %3D

A: Since you have posted multiple questions, as per our policy we will answer first question. Please…

Q: Find the solution of the following: 2. e2x(2cosy dx- sinydy) = 0; y(0) = 0 %3D

A: The given differential equation is e2x2cosydx-sinydy=0 It can be re-written as…