a) Solve the differential equation using separable method. b) Solve the differential equation using the method of integrating factor. c) Adjust the answer in (a) so that it matches the answer in (b).

Q: Solve the differential equation (D+ + 5D² + 4) y = sin x + cos 2x.

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Q: The Cauchy -Euler equation is a a differential equation with variable coefficients. صواب İhi

A: The Cauchy - Euler equation  is a linear homogeneous ordinary differential equation

Q: a) State the order of the differential equation and determine whether the equation is linear or…

A: This is non homogeneous differential equation.

Q: (2y2 + 2y + 4x²)dx + (2xy + x)dy = 0

A: Given differential equation is : (2y2 + 2y + 4x2)dx + (2xy + x)dy = 0

Q: dy = ay + by", dt a > 0, 6 > 0, -∞ < Yo < ∞

A: A differential equation is given by, dydt=ay+by2 for a&gt;0, b&gt;0, y0&gt;0. The objective is to…

Q: the differential equation of the gi u= A(sec4t)1+ B(csc4t)1 2x3 12 12-C

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Q: a.) y = 2cx² + c² b.) y = c1x + c2x² + sin x %3D

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Q: 3. a) Define Integrating Factor and Exact Differential Equation. b) Solve: (x2 + xy-y² )dx+ x² - 2xy…

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

Q: 3 tanx-2xy = c

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Q: (4r + 5)2 2- + tanzy= dr COSI

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Q: Form the differential equation by eliminating the arbitrary constant A, B from y=Ae?x+Be7*

A: We have to form differential equations

Q: Use direct substitution; verify that 2 X(+) = 6+² + t the following -3 is a Solution of differential…

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Q: The rate of increase in a bank account is 4% of the amount in the account; the initial deposit is…

A: Note: There are multiple sub questions. No specific question has been asked. So, We will solve the…

Q: Solve the differential equation  2y" + 60y = 2x2y" + 4xy'  . Then evaluate the Legendre polynomial…

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Q: Form the differential equation by eliminating constants a and b from y = a(b – z)(b+1) + 52. %3D

A: In this question, the concept of the differential equation is applied. Differential Equation A…

Q: 2. Determine the form of a particular solution of the differential equation. Do not evaluate the…

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Q: Give an example of a differential equation.  Identify its type according to linearity, form, order.…

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Q: dy Зх + у — 4 - 4 dx 2х + у — 3

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Q: Solve the differential equation 5y" - 5x2y" -10xy' + 100y = 0 . Then evaluate the Legendre…

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Q: 2 (x² + y² + 1) dx + x (x - 2y) dy =

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Q: Use order reduction to find the solution of the differential equation. 4x²y"+y= 0; y, = x² In x 1/2

A: Let y1(x) be non-trivial solution of differential equation y''+p(x)y'+q(x)y=0 and let…

Q: Form the differential equation by eliminating the arbitrary constants y = a csc x + b cot a

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