Evaluate: | (3y – 2)dx + y²dy C

Q: The particular solution of y+y-2y = e?x is

A: To find The particular solution of the given D.E.

Q: Find the solution. 2y" - 3y' + y = 0 (A By = c,e 1- ©y = c,e Dy =c,e

A: Find roots of  characteristic  equation  of given differential equation .If roots are real and…

Q: 2. (D² - 1)y = 2 1+ex

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Q: solve the equation 2xy" +xy'-y 0 5. 2 1 Does y() = x- real s y(1) =1, y'(1)= 2 solve the IVP

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Q: e a) y"+ by 19y x² + 1

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Q: O': what is the general solution of the equation. dy dr xy

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Q: d²y - y = у 3 10sin?x %3| dx2

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Q: dy - y = e2*y³ dx

A: Let's Solve,

Q: Find the solution. y'• ty ty" © y- (1-c, y- - (1-co")

A: We have to solve y'+ty=ty3 This can be written as: y'+ty=ty3⇒1y3y'+tyy3=t⇒1y3y'+ty2=t⇒1y3dydt+ty2=t…

Q: A. Find the general solution of y" = 12x². dy B. Solve for y F dx - 4 x²-1

A: The given differential equations A) y''=12x2 B) dydx=4x2-1 use the integration formulas,…

Q: Using Trapezoidal method √²³x² dx for n = 4 is equal to

A: The trapezoidal rule works by approximating the region under the graph of the function f(x) as a…

Q: A. Obtained the general solution. E... 10. (D² – 3D + 2)y = 3x²

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Q: Find the general solution of using the method of variation of parameters. d²y dy 2- - 42+ 2y = xe 2x…

A: Given,2y"-4y'+2y=xe2xComplementary SolutionAuxiliary Equation is 2m2-4m+2=0⇒m2-2m+1=0⇒m-12=0⇒m= 1 ,…

Q: d²y -6空+9= 0. dx2 dx 业

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Q: what is the general solution to the equation (o° +D)y (x) = x

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Q: Find the particular solution of -4y = 3x – 1 given that when x=0, y=0 and d2x dx dx II

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Q: Given that d²y 2. +y =0. dx2 Show that y = x is not Solution a

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Q: How do I integrate the following equation? U(z)=2.8*exp(-z/6300)

A: Consider the given equation as Uz=2.8*e-z6300

Q: I. Obtain the general solution of the following: a) (D2 + 3D + 2)y = 1 + 3x + x2 b.) (D2 − 6D +…

A: Use rules of differential equations

Q: Find the general solution y" – 6y'+9y=x*e*

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Q: 2x e dx 4e2a –8e* +5 -

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Q: b, y" -zy'-3y= e*

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Q: Solve the following d'y 8- + 16y = 9e2 dx? d'y dx4 using the method of undetermined coefficients.

A: The solution is given as

Q: Show that y %3D Cіx-1 + С2х + Cзlnx + 4x2 is a solution to x3y" + 2х?у" — ху' + у %3D 12х?.

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Q: 1 dz, C:k – 3i] = 3 z² +4z + 13

A: Since we only answer up to 3 sub-parts, we’ll answer the first 3. Please resubmit the question and…

Q: dx x² - 3

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Q: Find the general solution to  y''+ y' = 1 + 2sin(2t)

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Q: Find the solution to y - x+t y' = y if r(0) = 5 and y(0) = 4. %3D

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Q: e²–3¤ /1 – y² given that wher

A: Given that, dy/dx = e^(2 - 3x) . sqrt (1 - y^2) Then we get, dy/[sqrt (1 - y^2)] = e^(2 - 3x) dx…

Q: 50s d. F(s) = (s + 1)²(s² + 4s + 13)

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Q: Solve the Bernoulli's DE: 2x3 y = y(y? + 3x2). %3D

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Q: What is the general solution of ху(ху5 - 1) dx + х?(1+ ху)dy3D0 ? A 2x3y5-3x² = cy? B 2x°y3 - 3x2 =…

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Q: (D² – 3D + 2)y = e2*(1+e2x)

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Q: What is the particular solution if y(1)=D0? 1/2 xy = y+ (a² + y³)2

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Q: (2, 3), dy If x2 + xy = # = 10, then at the point dx

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Q: Find the value of d2y/dx2 at the point defined by the given value of t. x = t, y = square root 2t ,…

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

A: Please refer the attached image for complete solution.

Q: ~2V3 2/3 43 dx V16 – x² -

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Q: 2. (6x + y²)dx + y(2x – 3y)dy = 0

A: In this question, we need to check whether the given equation is exact or not and then find the…

Q: What is the solution of (2x - y)dx + (4x + y– 6) dy = 0? а. (x+у-3)°- с (2х +у- 4)? b. (x-y+3)²=…

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Q: Find the general solution of the following: 1. (D² – D – 2)y = 0 2. (D² + 3D)y = 0 3. (D² – 5D) + 4y…

A: according to our guidelines we can answer only three subparts, or first question and rest can be…

Q: What is the general solution of differantial equation?  Whicf of the options x² - y² + xy dy/dx =0

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Q: Find the general Solution of the diff. equ- x*y" +zxy-2y=D0 ?

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Q: 4s b. F(s) = s2 – 4

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Q: Use variation of parameters d²y +pdty+94=Fx) plem) to find a particular solution to y" – 2y - 15y =…

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Q: -13x b) y = S dx Integrate. x2-5

A: Explanation is given below..

Q: Function as, y (x) = (x² – 2) (3x + 2) %3D

A: Given,          yx=x2-23x+2

Q: 5 In(3x) dx 5ln (3x) +C 12. 4

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Q: | 8(x + 1) (2x2 + 4x – 1) dx 3/2 5.

A: For the given integral- I=∫8x+12x2+4x-132dx Let u=2x2+4x-1 Differentiating w.r.t. x to both sides-…

Q: Obtain a particular solution for + + +y = x³ + 2x + 1 dºy, d²y dx4 dx²

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Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.