e2x -1 If y = In find dx dy e2x +1 ' Select the correct response: 2e2x e4x+1 e2x e 4x+1

Q: Q2 /Find dy/dx, if: (1) x y+y =x2 (2) y = 3x* -5x' +10 у -

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Q: a. By differentiating x2 - y2 = 1 implicitly, show that dy/dx = x/y. b. Then show that d2y/dx2 =…

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Q: dy/dx - y = xy5 = 0 Ans. 1/y* = -x++ ce 4*

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Q: S16 -X2 メー dy dx + x?+yz

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Q: 5. (x* +a')dy= 2x| (x² +a²) +3y dx, where a is constant.

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Q: dy will be dx If y = (5x + 1)(2x-1 + In x), then

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Q: d'y dr2 dy - 2 +y=3 e4x, given y(0) dx 1 and y'(0) =4; 3.

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Q: a. (2ry*e + 2xy + y) dx + (r²y*e -x²y² – 3x) dy = 0; when x = -1, y = 1

A: As per our guidelines we are supposed to answer 1st question only. Please repost rest questions...…

Q: y(2x? - xy + 1) dx + (x - y) dy = 0, ANS. y(2x – y) = c exp (-x?).

A: Given differential equation is y(2x2-xy+1)dx+(x-y)dy=0

Q: d²y dx² - dy - - 6y = 0, when x = 0, y = 0, and when x = 1, y = e³ dx

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Q: Solve dy d'y -8 +12y = 0 dx? dx .2

A: The objective is to solve the above differential equation.

Q: If x^3+y^3=2, find the value of d^2y/dx^2 at the point (1,1). the value of d^2y/dx^2 at the point…

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Q: Find dy/dx If y ex A 2/א"e ],/איe D-2V B.

A: We have to find dy/dx.

Q: d²y dy y = e * is a solution of dx2 = 0 dx

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Q: Find dy dx dz 2 9=(z-3 Inax) a = constant

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Q: Obtain the particular solution when x = 1 and y = 1 yl? - y² + 1) dn - xlx? - y? - 1) dy = dx – x(x²…

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Q: The equation dy - ydx = [-x*y^3* e^(-2x) ]dx is linear in x but not in y. True or false?

A: Given that dy-dx=-xy3e-2xdx.

Q: dY X 5) Solve: dx Y(3) = 5

A: dy/dx = x/y This is a variable seperable differential equation.

Q: dy Find dx x = 7 y = 2-1

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Q: dy Find for x'y' +e2x = -3e" -1. dx

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Q: Solve the differential equation in Exercises

A: Given 17. dydx=2x1-y2 ,   -1<y<1 18. dydx=e2x-yex+y

Q: »4-x² 1-y- xe?y dy dx 4 - y (b) Ln(a² + y? + 1) d dy (a) 0, /1-y²

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Q: y = (ax-1) (6x.+5]%3 find dy dx 10

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Q: dy Find if dx y = 7u + 2 and u = 9x-3. dy dx Enter your ar

A: Given:    f(x) = 7u + 2       u = 9x - 3

Q: dy dx What is y(2)? Suppose = 6x² + 2x − 3 and y(0) = 4. - oy(2) = 14 oy(2) = 16 oy(2) = 18 oy(2) =…

A: The answer is given below:

Q: +y Evaluate dz dy dx 20 3 0 -3 0 00 -10 -4 0 10 -2 0

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Q: d²y d'y (k) 을-42+13y =0 (1) "+2+y = 0 dx dx? dx dx? d? (m) dx (n) 9 +16y=0 d'y dx?

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Q: dy Q2) Solve x- 2y = x³ cotan 2x dx

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Q: Q2/ solve; A: dy - = e* * y3 dx x+1

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Q: find dy/dx if x=(t2-2t+1)e3t and y=(t2+4t+4)e3t

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Q: dy y 5. Solve dx 5(x-2)y2 %3D (х- 2)

A: We first convert the given differential equation into the linear differential equation, then solve…

Q: y3 (3- e*)* dy dx

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Q: (c) Find the specific solution to d²y dx² when x = 0,= 0 and y = 1 +4 dy dx + 5y = 0

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Q: dy Find dx2 4 if y = x cos(x) d²y dx? ||

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Q: dy dzy If y = e2x –2e¬3x, Find at x = 1 dx 'dx2'

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Q: dy at t = 2. dx If x = 5t +4 and y = 3t° -7, then find а. 4 b. 1 с. 2 d. 3

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Q: Find 2," dy d²y dx ' dx? d3y and from: dx3 3. x = 1 – t? and y = 2t3 – t2 + 1

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Q: dy If =-x+4x -3 and y =2 when x =0 then y is equal to dx

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Q: dy Find of y = e4-3x + 63x*-2 x+5 dx

A: Given  y=e4-3x+63x4-2x+5 Find dydx

Q: 2-dy dy. y2 dx 12 ナ /2

A: We have to solve the given equation. The given equation is 2-dydX=y2X2+yX+1    ......(1)

Q: G3-y²sinx+303")dx+ (3xy² + 2ycosx + )dy = 0

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Q: dy 1. = e3x+2y dx X = 8; y = 1

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Q: Find dy/dx and d²y/dx2. x = e*, y = te-t

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Q: dy/dx=(x-7)e^(-2y) satisfy the initial condition y(7)=ln(7)

A: Use separation of variables to integrate.Given:

Q: d?y 7. y = e2" – 3e-, dx? dy - 2y = 0 dx

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Q: 2 dy 2- 2- y = e*/2y3 dx

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Q: dy dx + 4y - e* = 0, dr y(0) = 4 3

A: Given: dydx+4y-e-x=0, y(0)=43

Q: If y = (6x + 7)0.5(2.6x2 - 1.9), what is dy/dx?

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