(1) The general solution of the ordinary differential equation (p- x)(p – y) = 0 , (p = ) is (a) (2y +x- c)(y-2ce*) = 0 (b) (2yx² - c)(y- ce") = 0 (c) (2y +x + c)(ye*) = 0 (d)(2y – x²-c)(y-ce") = 0

Q: show that function  y1=x-1 is a special solution of the differential equation y'=1 - ( y-x+1)2 and…

A: Given the differential equation y’ = 1 – ( y – x + 1)2 and we have to show that y  = x -1 is a…

Q: Consider a nonhomogeneous differential equation y" + 4y = -12x + 10e-*. (a) Verify that yp = -3x +…

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Q: -y(0)-0, x(0) = 0, y (0) - em of differential equations can be e first order with the help of the…

A: Given as, x¨= y˙ -1 . , y¨=-x-2      u=x˙ and v=y˙       u˙=x¨  v˙=y¨

Q: The solution of the differential equation (xy – y²)dx – (x² +y²)dy = 0 is : A) 2 In + 1|- tn -;…

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Q: 6. Given a differential equation with coefficients linear in two variables. If the DE represents…

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Q: 1. Find real-valued fundamental solutions of the differential equation 1 x' = Ax, A= 2 %3D 4 -3

A: We need to find the solutions of given differential equations. Given - X' = AX, where A = 1-24-3 So,…

Q: The general solution of the second-order differential equation y"-y-12y = 0 is: y = c₂e³x + c₂e-4x…

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Q: 7. Find the particular solution of the differential equation dx +5x³y x³ passing through the point

A: Given, dydx+5x3y=x3,   0,72 it is a linear differential equation p(x)=5x3,  q(x)=x3…

Q: (4) a general solution of the 4th-order differential equation y +y(3) + y" = 0.

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Q: 1. Verify that for constant C the function ø(x) = + Cx is a solution of the differential equation 2…

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Q: 2-The exact solution of differential equation ý--4y with y(0)-1 is (a) 2e-4x (b) e-4x (c) e-4x +1…

A: As per as our guideline i am supposed to answer only one question from all these question . To get…

Q: Show that the y1 = x-1  function is a special solution of the  y'=1 - (y-x+1)2 differential equation…

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Q: The equation y" + y'- 2y = x² is called a differential equation because it involves an unknown…

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Q: A 2nd​ order, homogeneous, constant coefficient differential equation has characteristic roots​ x=-1…

A: Please find attachment for the details solution

Q: For the differential equation (x² – 4)y" + (x – 2)y' + 2y= 0, the singular points are: %3| x=2 and…

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Q: Show that the function  y1=x-1 is a special solution of the differential equation y'=1-(y-x+1)2 and…

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Q: 2. Prove that the given first order ordinary differential equation (2x – y) dx – (x – 2y) dy = 0 is…

A: A detailed solution is given below

Q: A differential equation (of any order) is homogeneous if, after collecting all the terms involving…

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Q: Find: a) general solution of the differential equation xy' - y = xln x ( x> 0 ); b) particular…

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Q: 1/2 y'' + y' + y = 0  y(0) = 2 y'(0) = -1/2 Solve differential equation using initial values

A: Given differential equation is: y''+y'+y=0The auxilary equation is:D2+D+1=0D=-1±12-4×1×12=-12±i32

Q: 2. Use variation of parameters to determine the general solution of the nonhomogeneous linear…

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Q: 2. Test the exactness and obtain the general solution of the differential equation: 2+yexy y' =…

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Q: A first order Bernoum's differential equation is in the form 2. The Bernoulli's form of the…

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Q: Example 8 : Form the differential equation by eliminating the arbitrary function ƒ fromn xyz = f (x2…

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Q: Find the particular solution that satisfies the differential equation F'(X) = 10x − 12x3 with an…

A: Given the differential equation: F'x=10x-12x3 Initial condition: f3=2

Q: A model of a spring/mass system is 4x" + e0.1x- 0. By inspection of the differential equation only,…

A: Given - A model of a spring/mass system is 4x'' + e-0.1tx = 0. To find - By inspection of the…

Q: 5. If the characteristic equation of the differential equation 27 - 184 dx +8- y-0 is dx 27m -18m…

A: The characteristic equation of the given differential equation is 27m4-18m2+8m-1=0.

Q: Obtain the particular solution of (3x2-2y2)y'=2xy; when x=0. y=-1

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Q: For the differential equation (x2 – 4)y" + (x- 2)y' + 2y = 0, the singular points are: O None of…

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Q: find serious solution of differential equation (x+3)^2y''-9(x+3)y'+25y=0

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Q: Please, reply as soon as posible! Determine the general solution of the differential equation y ′ ′…

A: To find its general solution for the below differential equation. y''−16ky'+64k2y=ex

Q: 5. A differential equation is if it can be written in the form f(y)d(y) = g(x)d(x)-

A: A differential equation is ORDINARY if it can be  Written in the form f(y)dy = g(x) dx .

Q: (9x^2 + y - 1) - (4y - x)y′ = 0

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Q: Yp = -1 / 5ex - 1/2 (cos 2x) ((ln (sec2x + tan2x)) is the particular solution of the differential…

A: A solution yp(x) of a differential equation that contains no arbitrary constants is called a…

Q: Obtain a linear differential equation with real, constant coefficients that is satisfied by the…

A: If the particular solution is: y=2excos3x                                        ....(1) The first…

Q: (y-x)y'=y-x+ 2; y=x+2√√√x+5 When y = x + 2√x + 5, Thus, in terms of x, (y-x)y' = y=x+2= Since the…

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Q: 5. (a) Find the particular solution of the differential equation x³ = 1-e²t if x(0) = 2.

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Q: The solution of the differential equation y^'=-2xy is a family of solutions of

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Q: Find the particular solution of the differential equation y’ + 7x = 0, at y = 0, x = 3. y = 63x2/2 y…

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Q: find the solution of differential equation 2 y3 y' +- y

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Q: Choose a solution for the differential equation y'' - y = x2ex + 5: e-x(1/6x3 - 1/4 x2 + 1/4x + 3)…

A: Given non- homogeneous differential equation,y''-y=x2ex+5  ...(1). Solving the homogeneous part:…

Q: The differential equation: y²x + y² = x²yy' is solved by

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Q: 5) Find a homogeneous linear differential equation with constant coefficients whose general solution…

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Q: 3. The differential equation = 8 – 2y can be solved using the method of separation of variables or…

A: solve using separation of variable dydt=8-2y dydt=-2y+8 dydt=-2y-4 dyy-4=-2dt take integration…

Q: y" – 2y' + y = -3 - x+x².

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Q: A solution of a differential equation that is free of arbitrary parameters is called a/an solution.

A: Particular solution.   A solution of a differential equation that is free of arbitrary parameter is…

Q: The General solution of differential equation defined by: x2 y"-2x y'-4y=0 is defined by 1 y(x) = C,…

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Q: of the differential equation у" - Зу' + 2у %3е-2t

A: Introduction: A differential equation is a mathematical equation that contains one or more…

Q: 1. Discuss or show the methods in solving Exact and Non-Exact Differential Equations.

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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.