6. The slope field for the differential equation dy x²y + y2 4x + 2y dx will be undefined (have vertical segments) when (A) y = 2x, only (B) y = -2x, only (C) y = -x², only (D) y = 0, only (E) y = 0 or y = -x² %3D %3D

Q: y' = (1-x)y²+(2x-1)y-x a special solution of the equation y1(x)=1, Find the general solution of the…

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Q: 40. Let y = 3x? - 2x + 1. Use differentials to find the ap- proximate change in y when x = 2 and Ax…

A: Consider the function y=3x2-2x+1. Need to find the approximate change in y when x=2 and ∆x=0.05.

Q: y' = et ; y(0) = 2 find the general solution

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Q: y = x"^, x > 0 Inx-1 Inx Inx C. y'= 2lnx x' „Inx-1 D. y'= 2lnx x" „Inx-1 A. y'= x B. y'= 2 x'

A: SOLUTION-

Q: Find the derivative of 4x - 9y = 17 9x y' = 4y -4x y' = 9y 9x 4y 4x 9y

A: Given problem:- Find the derivative of 4x² - 9y² = 17

Q: How do I find the particular solution yp in the equation above?

A: For particular equation we will crate function for particular integral. Then we solve it by using…

Q: dy-(2y xe+2x²yex) dx (6 y3x -2x² e%) 1 the generl solution of the differential tion.

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Q: y' =xy

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Q: 3. (2x – y)3 = 3x?y, find y' %3D

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Q: x'+1 y3= r+1 1. and x+3y = 7 %3D

A: Please refer the attached image for complete solution.

Q: 2. (x2) y = y+2(x2)

A: Topic = Differential equation

Q: 1. Find a general solution of the first order equation: y'= 3x²y².

A: The given first order differential equation is solved by method of separation of variable.

Q: Solve for y. y' = 7x + xy; y = 5 when x= 0 y =

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Q: G(y) = (y − 1)4 / (y2 + 2y)7 Find G'(y) =

A: for a polynomial function of power n: Division rule of differentiation:         Chain rule :…

Q: Bernoulli Equation (17) y'+ () y = x³y³ (18) y' + 3x²y = 4x²y² (19) (x²yª – 1)dx + x³y³dy = 0 (20)…

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Q: x+ dy If y = then will be %3D 2x-3' dx (2x – 3) (1 –) - (2x +) A. (2х - 3)2 (2x – 3) (1 +) – 2 (x+±)…

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Q: Inx+1 dy will be dx If y = then 2x3 – 3x' (2x³ – 3x) +1) –- (In x + 1)(6x? – 3) А. (2x³ – 3x)² (2x3…

A: Using derivative rule of (u/v),

Q: If y= X 1-x +7x+9, find y' .

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Q: Verify that y = x² – 1 is a solution of (y')* + y² = -1. %3D

A: Given;            y=x2-1 is a solution of y'4+y2=-1 We compute the first derivative.…

Q: 1. Use the basic differential properties shown in section 3-5 to find each indicated derivative. (A)…

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Q: Identify if the differential is homogenous or heterogeneous. State also whether the equation is…

A: As per guideline we have to solve three subparts

Q: Find y' y= y" = 3x + 4 2x-3

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Q: dy/dt = y(1-y) y1(0) = 9, y2(0) = -1 What do y1 and y2 mean? The first and second derivatives?

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Q: Find the first derivative. (a) y=x* (b) y =xnx 2.

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Q: ii) Solve (x D²– 3xD+4) y = x² given that y(1) =1 and %3D - y'(1)= 0.

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Q: solve: y'' - 5y' + 4y = 20cos(2x) + 30sin(2x) y(0) = 1 y'(0) = 3

A: We have to solve the differential equation given below : y'' - 5y' + 4y = 20cos(2x) + 30sin(2x) ,…