Ex:Salve the d.fferential equation (3x-y-1)dx-(X-y+3)dy-o

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

A: The given equation is

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A: The given differential equation is  dy/dx + 3x2y = x2 y(0) = 2

Q: dy Given y = x" In (2x), determine dx a.x“-' In (2x) + а-1 None

A: Please refer to the image below

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Q: 6. f(x, y) dx dy

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Q: of x = Y ? x+y dy x-y Q2 Find dx

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Q: y(3x-2)dx +x (1-2 y)dy=D

A: We will solve the problem

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Q: 2х-1 dy if y=f and f'(x)=sinx²,find dx x+1

A: According to chain rule of differentiation if f and g two functions are differentiable and function…

Q: 1-y2 Q2: Evaluate i y² (x? + y²)dx dy

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Q: 2e2x -1 Let y = %3D et dy Find dx

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Q: 3) y tan-1(y²) dy

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Q: d?y Calculate dx2 y = e-X + eX d?y dx2

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Q: (x - ky) dx +k(y-x)dy=0 where k 3t7

A: Given :(x-ky)dx+k(y-x)dy=0where k=7+3=10

Q: Show that y=xe-x satisfies the equation dy/dx +y=e-x

A: We find dy/dx using product rule

Q: The domain (Dx) of y = 1 Vx-1

A: We have given ,         y = 1x-1 As y is under the square root its means y ≥0 .

Q: d² y If ax? dx? 3. Find + 2 hxy + by = 1, h? - ab Ans. (hx + by)

A: So in this we have to differentiate twice. I'm providing hand written solution.

Q: y= 2*+☆ -3 sec x; find dy

A: As per Bartleby answering guidelines if multiple questions are posted in a single picture then an…

Q: C. Bernoulli's Equation 5. (y* – 2xy)dx + 3x²dy O when y(1) = 0

A: We have given a Bernoulli differential equation.

Q: dy = 2x y? + 3x²y², y(l)= -1 26. dx

A: by separable variable

Q: dy If y = x (e* - 1), then %3D 6. dx

A: Given: y=x^2 ((e^ x)-1) To determine: d y/dx

Q: dx – x' csc 2 ydy - dy tan 2 y

A: Given that:

Q: b. Given that y=2x - In x find expressions for d y and dx a. dx

A: we have,  ddxxn=nxn-1ddxlnx=1xddxaxn=addxxn

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

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Q: /16- y? (x² + y?) dx dy 0 Jo

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Q: d²y - = 0 and dx? Let y=e" +b(x+1)'. When x = 0, that dx dy a) suppose = 0. Find the possible values…

A: Here we have to find the values of a and b. The solution is following .

Q: dy :- y = e*y2 dx

A: Given equation is

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Q: ution to dx = 1+t-x- dt 2 +C +C) /2-C

A: We have to choose the correct answer from the given options according to the given information

Q: Classify then solve x(x - 1)dy - ((x-2)y + x*(2x- 1)) dx o

A: We will find out the required general solution.

Q: ľ V2x + I dx S" x e*-1 dx

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Q: dy d'y dr -(금+1). When x-4, = 6 and when x = 4, y = 0. dx Find y in terms of x.

A: Here we will find out the required expression .

Q: iven the ODE, solve: x(x + 4)*dy + [y(x+ 4)* – 3x*y³]dx = 0

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Q: The equation dy – ydx = [-x * y^3 * e^(-2x) ]dx is linear in x but not in y. O a. True O b. False

A: We have to determine whether the given statement is true or false

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

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Q: dy when x = 1. dx If y = u" and u= 6x +6, find (Simplify your answer.) dx x= 1

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Q: Evaluate dy if y = (2x + 1)3/4, x = 1, and dx = 0.03. What quantity does this answer represent

A: Given  y = (2x + 1)3/4,  x=1 and dx = 0.03  We have to find dy

Q: dy -4 when x = 2 and dt 7 If 3x?y + 2x = – 32 and dx y = - 3, find dt

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Q: (iii) dx 4-y: (1)y(0) = 1, (2°)y(0) = 5

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Q: dy If y = (x- 1) e* then dx2 %3D O A.

A: Derivatives can be defined as rate of change of function with respect to an independent variable. It…

Q: dy = a-x dx when x 1, y = 2 when x = 2, y = 0 %3D what is the value of a?

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Q: Jo (2x - y) dx + (x + 5y) dy. C: x-axis from (0, 0) to (0, -5) and (0, -5) to (3,-5) X Evaluate -30

A: Here we have to evaluate        ∫c(2x-y)dx+(x+5y)dy    C: x-axis from (0,0) to (0,-5) and (0,-5) to…

Q: d?y dy + 4- 2- +12 y 2x2 sin(x) - e2x dx2 dx

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Q: find explicit solution: x^2 dy/dx =y-xy       y(-1)=-4

A: Given differential equation is                                       here we can easily separate the…

Q: QI/ : If . Find dy y = 2v3 +- v = (3x +2)/3 , dx

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Q: x =rcos(0( , y ناتج السؤال الأول: جد باستخدام التحويل )0)rsin= التكامل e-(6x+5y) dxdy

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