d.) (y³ + x ln ) dy + (y In ) dx = 0

Q: Solve the differentian equation dy - 54 dy + 6y = 0. dx? dx Show that the functions you obtained as…

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Q: 6. Find the solution of 1 dy + y = da 3+ e

A: Given dydx+y=13+ex

Q: 2. Use separation of variables to solve the following equations: (a) (y² + 1)dy + (e² + x)dx = 0.

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Q: 2) Determine the constant A such that the equation (x² + 12ry) dx – (Ar² + 8y) dy = 0 is exact and…

A: The differential equation P(x,y)dx+ Q(x,y)dy =0 is an exact equation if and only if…

Q: 3. Show the equation (1+ e*y + xye*)dx + (xe* + 2)dy = 0 is exact and solve it.

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Q: Find the general solution of the given Attached equation

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Q: . Solve the following Ricatti equations: 2 y - y² = -x², given that y₁ = x² is a particular dy dx…

A: *By Bartleby policy I have to solve only first one as these are all unrelated problems.These are all…

Q: Use the variation of parameters to solve the following equation: d^2y/dx^2- 3 (dy/dx)+2y=cos⁡(e^-x)

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

Q: dy = y? – 4 dx

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Q: Find the general solution to the following equations: dy у-х dx y+x

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Q: The solution of the DE dy + (y – 1) dx =0

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Q: Solve the following equation and show that it is exact 3x (xy +2)dx + (x^3 - 2y)dy = 0

A: Given differential equation is  3x(xy+2)dx+(x3-2y)dy=0

Q: solve the DE b

A: The DE is (x-y+2)dx-dy=0or, (x-y+2)dx=dyor,dydx=x-y+2

Q: dy +xsin 2y = x cos² y. dx Solve the Bernoulli equation.

A: Given: y' + xsin2y = x3cos2y ⇒y' + 2xsinycosy = x3cos2y ⇒y'sec2y + 2xtany = x3 Now, let tany = v ⇒…

Q: Find an integrating factor and solve the given equation. (12x + 3) + (4²+¹2) = 0 12y dy dx

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Q: solve D.E. by using Linear (y? + 1)dx + (2xy+ 1)dy= 0

A: See the attachment

Q: -2y -2y (²²7) dx + e dy = 0 ex + x

A: Different ial eq is homogenous.

Q: 5. Solve the 2nd- order differentinl equation: d'y dy dr +2 +y=e24 CS Scanned with CamScanner

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Q: (xy)dx + e*dy = 0, as xo, y =D;

A: Given:- (xy2) dx + ex dy=0 To find:- Particular solution of given differential equation

Q: Q2. Find the general solution of the equation. dy 2(1+y?) dx Find the particular solution that…

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Q: Use appropriate substitution to reduce the following equation to a variable separable and then Зх +…

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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: Obtain the general solution to the equation. dx + 4x = 2y7 dy The general solution is x(y)=,…

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Q: Find f(x) in the equation y sin x + y f(x) = 0, then solve for the general solution of the resulting…

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Q: + 6x)dx + (ln æ – 2)dy = 0

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Q: (1 + y²) dx + (x²y + y) dy = 0.

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Q: Test the exactness of the following equation then solve the equation: y In(y) dx + (x – Iny)dy = 0 -

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Q: 1. Find the general solution of (y? – 1) = 4xy? dy %3D dx

A: Topic:- differential equations

Q: Q5. Transfer the Cauchy-Euler equation to a constant coefficient equation and find the general…

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Q: x(xy – 1)dx + dy = 0 (Non-exact)

A: Solve differential equation.

Q: Find the general solution of the following exact differertial equation (e Ax + 2xy²)dx + (cos y +…

A: Givne that  The following differential equation  (e^4x+2xy^2)dx+(cosy+2x^2y)dy=0  To find the…

Q: d²3 Find the particular solution of +16y=0 if given y(0) =1 and y'(0) = 0. +8 dx dx

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Q: Find the general solution of the following equations? 1- e* (y – x)dx + (1 + e*)dy = 0

A: To find the general solution ex(y-x)dx+(1+ex)dy=0

Q: 3. Find dy of the following equations: dx a. y = |(e-3x² + 7x² + In 8x

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Q: The µ(x) that converts the equation below into an exact equation x dy (x*ev ++ (2x²e" + 1) = 0 y) dx…

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Q: Obtain the general solution to the equation. dy + 9x +8 - dx The general solution is y(x) = ,…

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Q: Find the values of "a" such that f(x,t) = e ax + 6t satisfies the equation of 2f ot dx? smallest…

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Q: Q1) solve all these first order diff questions with appropriate method of solutions dy _ y²+xy?…

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

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

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

Q: 1) 1+e" |dx+e" (1- xydy =0

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Q: 35. Find a value of the constant k so that kx²y dx dy = 1.

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Q: (ylny – e¯xy)dx + ( + xlny) dy = 0

A: Solution :-

Q: dy A. dx ay = xy', y(0)=1

A: Hey, since there are multiple questions posted, we will answer first question. If you want any…

Q: 1. Solve the following equation dy dx x = x² + 3y, x>0

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Q: 10. Given that y = at x = 1. e* X + 1 Find, in terms of e, the values of . 최 and dx dx²

A: (10). Given: y=exx+1   As we know that; The Power law; ddxxn=nxn-1 The Quotient rule;…

Q: 11. (x In y + xy) dx + (y In x + xy) dy = 0;

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Q: Determine the constant A such that the equation (x2 + 3xy) dx + (Ax² + 4y) dy = 0 is exact and solve…

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Q: Substitute y=y1+z  and dy/dx=dy1/dx + dz/dx into  dy/dx = P(x)+Q(x)y+R(x)y2 to get a Bernoulli…

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