Solve the follawing D ·E. 2. y²dx + (3xy +y²-1) dy =0

Q: Find the general solution of the equation x(y2 + 1)dx + (1+ x²)dy = 0. A. In(x2 + 1) + 2Arctan y = c…

A: The given equation is; x(y2+1)dx + (1+x2)dy =0

Q: Solve (x+2y-1)dx + (2x+y+1)dy = 0

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Q: If z = 3x? + y? – 5y, find the differential dz. You should have variables dx, dy, y, and x in your…

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Q: 3. (x² + 6y²)dx – 4xydy = 0 , y(2) = 1

A: Problem is in the form of homogeneous form...so put y=v.x and proceed as I have done solution step…

Q: 5. Find the general solution of the given DE: 2x + 2xy2 y + 2x?y dy dx

A: First We will separate X and y terms of the given differential equation and than integration gives…

Q: SIder ne DE dy dy 6y = 12x, y(0) = 1 dx dx? Ae2 1 is a solution of the DE and determine Verify that…

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Q: Q6: Determine a particular solution of the equation d'y +4y 4x cos 2x dx Using D-operator method

A: The solution is given as

Q: (D² + 1) y = x cos a

A: NOTE: Refresh your page if you can't see any equations. . for the homogeneous system, the…

Q: y = asin(k(x – E %3D

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Q: Solve the IVP (2xy?+4)=2(3-x²y)- y(-1)%3D8 the constant Cis dx

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Q: d?y Example: Solve the D.E. + 2 dx2 dy + 2y = 0 dx

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Q: dr - (x- 2) ey dy = 0

A: Given Differential equation is linear. We will solve it by finding integrating factor

Q: (9cosx+y°cosx) dx +2ysinx dy = 0, y(5)= -4 the value of the constant (c) of this D.E will be:

A: Solution is written in below steps.

Q: What is the annihilator for y=x e*cos 2x ? (D²+5)2 ® D² +5 © (D²-2D+5)2 D D2-2D+5

A: See the solution.

Q: Bessel equation d²y dy +2x- + (x² – 4)y = 0. dx? dx

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Q: Find dy/dæ in terms of t if x = te', y = -2t – 2e dy/dx = %3D

A: topic =derivative

Q: 3 – 6xy – 2y) dy = 0 ху Find the general solution of (ye - 2y) dx + (xe А. eу + 2хy3 - у? %3D с В.…

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Q: B) Find the general solution to the following DE. dy y? + x2 = 0 dx

A: Given differential equation is y2+x2 dydx=0

Q: /2 ( 2) (2a- z) dr x2) ? dx • B I A , E E E E 8 &

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Q: Using Bernoulli's equation , find the solution of DE:  4xy dy/dx = y^2 + x^2 ; initial condition…

A: The solution follows as:

Q: Solve the Ro liowing B E 2 X + 2 -zey= zX

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Q: Find the solution. 1. ху3dх + (у + 1)e-*dy — 0

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Q: (2xy +y) dx + (x²- x ) dy = 0

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Q: 1+y Determine the solution for the given DE: + zy?(1+x*)

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Q: (b) I xy(z +2) dx dy dz

A: We need to evaluate the given triple integral. Note the integration result ; ∫undu=un+1n+1+C , C is…

Q: Is the equation separable, linear, bernoulli, or homogenous? x4 + 4xy2 2x3 + x²y +y³ а. dx = x* +…

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Q: Is the equation separable, linear, bernoulli, or homogenous? dy а. dx x4 + 4xy² 2x3 + x²y +y³ b.…

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Q: non m Q4) Solve the D.E= %3D dx ya

A: Differential equation

Q: y = sec ¹3x, find dx VAL dx (4) 1-1 - A VE!! (e) None of these

A: Solution

Q: What is the answer for this DE? 1.) (y -

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Q: So S (2x + 3z – y). dz. dy. dx B- Solve

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Q: 2. Obtain the particular solution when x = 1 and y = 1 y(? - y? + 1) dx – x(x² - y? - 1) dy = xlx? -…

A: Here is the solution of the given differential equation.

Q: The solution of D.E " -y = 5(t – 1) ,y(0) = 0,y'(0) = 0

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Q: How do you solve.  The question is... Assuming x and y are functions of t.  What is dy/dx for each?…

A: Given information:The given function is 2xy – 5x + 3y3 = –51.Both x and y are functions are t.The…

Q: Solve the exact equation + 2x )dx + + 2y )dy 0. The solutions are of the form F(x, y) c, where %3D…

A: Given;

Q: 1. The function u(x, y) = e cos y is a solution of: %3D a) dx² dy? b) = 0 dy? Pu c) + 4- d) None of…

A: 1 Given function is ux,y=excosy. Differentiate ux,y=excosy partially with respect to x…

Q: What is the annihilator for y=x e*cos 2x ? A (D2-2D+5)2 B (D2+5)2 © D2-2D+5 (D D2 +5

A: A detailed solution is given below.

Q: (c) Test for exactness and solve the IVP, critically outline the particular solution (x + 5e*y)dx =…

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Q: y? – a? -, y(1) = -V2 dx dy xy

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Q: Solve the diffrential equation.(pls step bu step and clearly) (d/dx+2x)(dy/dx+2xy)=2e^(-x^2)

A: We have given differential equation is…

Q: Solve the Bernoulli equation dy + xy = xy dx y = (ce²² – 1)-} .B y = (ce² +1)-} .C y = (ce²² + 1)-}…

A: Thanks for the question :)And your upvote will be really appreciable ;)

Q: Is the equation separable, linear, bernoulli, or homogenous? dy а. dx x4 + 4xy2 2.13 + x²y +y³ b.…

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Q: Example:- Solve the equation Н. W. (3y + e*)dx + (3x + cos(y))dy = 0 dy 2) 1+y? +3x2y 1-2ху-х3 1) dx…

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Q: Find the complete solution First order DE dy = 2y3-ye dx Xe^y -6xy²-2y

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Q: Solve the equation. (+5x) dx+ e*y dy = 0 An implicit solution in the form F(x,.y)% C is =C, where C…

A: To solve: The equation x3+5x3y4dx + ex4y3 dy = 0 .

Q: What is the annihilator for y=x e*cos 2x ? A D2+5 B D2-2D+5 © (D²-2D+5)2 (D² +5)2

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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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Q: (15pts) Identify (write down) the type of DE, and find the general solution. (y- 3x)dy = (x +3y)dx…

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Q: If z = 52? – 3y? + 4y, find the differential dz. You should have variables dz, dy, y, and z in your…

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.