Topic: Substitution Suggested by the Equation 1. 4(3x + y - 2)dx -(3x + y)dy = 0

Q: 4. (у- 2ку + 6x) dx - (x?- 2ху + 2) dy -0

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Q: dy-3x²e-3x dx = 3y dx

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Q: Equations). =x (1 – y²) 2 + 5y + 2x + 10 2ху — 10у — х +5 -dx + -dy 2х + 3 у — 6

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Q: (х- 4y - 3) dx -(х-бу— 5) dy %3D о ans. (x - 2y - 1)? %3D с (х-Зу- 2)

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Q: (a) (3-x- y)dy=(2x – 4y+6)dx.

A: According to the guidelines I can solve 1st problem only. For the remaining problems you have to…

Q: (3y? + 2)2 = 1 and y(-1) = 1 What is x when y = 2? %3D dx

A: solve the differential equation by separating the variable and integrate it.

Q: 3. (10 – 6y +e 3) dx -3x 2dy = 0 -

A: According to our guideline, we can solve only first question of multiple question. If you want…

Q: Diferential equation: d'y dy dx + 2y = 0. dx Auxiliary equation: m? - 3m + 2 = 0.

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Q: dx y x = 2y, y(1) = 5 dy

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Q: Question 2 Consider the equation 3xy + y? – 2x = 1. Find dy - dx Зу— 2 За + 2у - O 2– 3y 3x + 2y Зу…

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Q: (i) 2y (ii) 0. dx

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Q: 3. dy = (x - 3y)dx ans. 9y = 3x - 1 + ce 3

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Q: Topic: Subtitution Suggested  by the equation 1. (2e^(2y) - x)dx = 2e^(2y)(e^(2y)+ 2x)dy

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Q: (2х - Зу+4)dx+ 3(х - 1)dy %3D 0; x(2)- 3

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Q: Description 1. (2æ3 – xy? – 2y + 3) dæ – (x²y + 2x) dy = 0 - - -

A: Here I am attaching image so that you understand each and every step.

Q: x-2 4. Using substitution method to solve dx? Please x+1 identify u and find du. Then solve problem.

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Q: 8. (y- 2x)dx - x(1- xy)dy 0 Ans.

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Q: Question 4 Find the solution. ,dy 2- y?=2xy dx (A 2x -2 B

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Q: dy -x-ly=²sin2x dx || 2 . 2号=2でッる xp

A: First order differential equation of the type, dydx+Pxy=Qx can be solved as follow: 1. Find…

Q: Example 2. Solve the equation y(y* – 1)dx + x(y +x)dy = 0 Answer: 2ry – a? = cy %3D

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Q: Linear First-Order Equations y dx = (e + 2xy – 2x) dy |

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Q: Give a geometrical explanation of why

A: Consider the given integration as ∫aafxdx=0

Q: solue 2/2y² + 5xy - 2y +4) dx + x (2x +2y-1) dy = 0

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Q: 2) (-4у + e-3*)dx %3D 4 dy

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Q: 4. Substitution Suggested by the Equation: (x+2y-1)dx+3(x+2y)dy=0

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Q: Homogenous Equation y? dx – (2x? + 3xy) dy = 0 Final answer should be in terms of y

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Q: (3-9)dx + 쁜dr + dy =0, y(-1) = 2. (y¯2x) ry²

A: Given: 3-yx2dx+y-2xxy2dy=0, y(-1)=2

Q: y4 – 2xy) dx + 3x²dy= 0

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Q: Q-11 Find the order and degree of the d 3 - d²y \ 2 equation V - 4 = 0. dy dx - dx?

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Q: Example 8. Solve the equation y*dx + (3ry+ y – 1)dy = 0

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Q: dy +2x². dx3 dy dx2 + x- dx - y = 0

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Q: 1. 3(3x? + у?)dx — 2ху dy %3D0

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Q: ubstitution suggested by the equation (3x-2y+1)dx + (3x-2y+3)dy= 0

A: Given that:  (3x-2y+1)dx + (3x-2y+3)dy= 0

Q: a) esin 7z dx 2e-2 b) lim 5x 2e-2 c) Sx+5 I-0 5x+5

A: Since you have asked multiple sub parts, according to our company guidelines we are supposed to…

Q: Solve the equations. 1. (2x - y)dx + (4x + y- 6)dy = 0 2 (x+ y-1)dx + (2x + 2y + 1)dy = 0

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Q: 3 I= |(e* +x² + A\dx Дх 3D0, 25 1

A: Solve the following

Q: 4 y = (-2а —4) 3 1 Find dy/dx

A: We will further simplify the function and then differentiate it using the chain rule of…

Q: 6- 2 dx 子 メt Casy =0.

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Q: 2- (2xe + e*)dx + (x² + 1)e'dy = 0 %3D

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Q: 2. (бх * у) ӑх *у (2х- Зу) dy - 0 3. (2xy– 3x²) dx + (x² + y) dy = 0

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Q: IV. Substitution Suggested by the Equation 1. (2x + y)dx- 3(2x+y+4)dy=0

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Q: ( 3х — у +1) dx- (9х- Зу — 3) dy %3D 0

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

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Q: Homogenous equations y? dx – (2x? + 3xy) dy = 0 (Final answer should be in terms of y)

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Q: dy - (1 + л)у — ху" dx

A: we have to solve the given differential equation

Q: 1. What is wrong with the equation dx -1 23

A: Since you have asked multiple questions in single request  so we  will be answering only first…

Q: Obtain the general solution to the equation. dy - Y + 6x +5 dx

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Q: Solve the equation. dy dx dx -- dy %3D

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Q: 9 - 1 || (6x + y) dx dy = (Simplify your answer.) 0 - 2

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