The integrating factor µ(x) of the differential equation: dy (x In x) + y = 2 In æ is In x H(x) = Ou(x) = x ln a In x u(x) = In a u(x) = In(In a)

Q: (4) Form the differential equation by eliminating the arbitrary constants a and b from y=ae +be¯ª.

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Q: What is the integrating factor for the linear differential equation 2(y - 4x^2) dx + x dy = 0?.

A: Given:  2(y - 4x^2) dx + x dy = 0

Q: The Bernoulli's form of the differential equation 2x³dy-− y(y² + 3x² ]dx = 0 is

A: As per our norms we have to write one question at a time kindly repost remaining questions.

Q: The differential equation governing the decay of a certain radioactive substance through time is dq…

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Q: Solve the Attached problem ?

A: dydt=Kydyy= K dtIntegrate both side ,∫ dyy=∫ K dt

Q: What is the particular I solution of the differential equation (2x + y²) dx + 2xydy = 0 when x = 1…

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Q: 3. Show that the differential equation dx is homogenous. Zxy

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Q: Form the differential equation whose primitive is given by y= ex(a cos⁡x + b sin⁡x),  a, b, being…

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Q: From the partial differential equation by elimanating the arbiraty function z=f(x2+y2+z2)

A: We have to form the partial differential equation.

Q: An object of mass m falls from rest and its velocity v given by dv =mg - kv v(0) =0 dt -- where k is…

A: Consider the given equation. mdvdt=mg-kv Further, simplify and make for integration.…

Q: Since dv = cos( cos9 x) dx, integrate the differential equation to obtain the function v. V = ^p -…

A: We have to find solution

Q: (4) Form the differential equation by eliminating the arbitrary constants a and b from y = a sin x…

A: Eliminating arbitrary constants a & b using derivatives.

Q: A circuit consists of a resistor of resistance R and a capacitor of capacitance C, connected in…

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Q: Consider the differential equation y"+ya+x. If g(x) is a solution of the differential equation…

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Q: In a differential equation where y is the dependent and x is the independent variable and the…

A: In a differential equation where y is the dependent and x is the independent variable and the…

Q: A stream, which is polluted with insecticide at concentration 8 g/m³, flows at a rate of 24 m³/day…

A: Concentration=8 g/m3 Flow rate =24 m3/day Volume =1800 m3 Initial insecticide concentration in the…

Q: Obtain the differential equation associated with the given non-derivative equation in x and y. Show…

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Q: Biotransformation of an organic compound having concentration (x) can be modeled using an dx + kx2 =…

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Q: verify that the given equation is a solution of the differential equation.(elimination of Arbitrary…

A: The solution is given as  y=-cos(x) ln(sec(x)+tan(x))                   (1) Differentiate equation…

Q: Form a differential equation by eliminating arbitrary Function. Z= (x + y)f(x² + y² ) %3D

A: Given z = (x+y)f(x2+y2)zx+y = f(x2+y2)                             (1) Partially differentiate with…

Q: In a city of a fixed population of "P" people , the rate of change (with respect to timet) of the…

A: Given Data: A city has a fixed population is P. Also given, the rate of change (with respect to…

Q: Suppose a student carrying a flu virus returns to an isolated college campus of 3000 students.…

A: Total no. Of students=3000 And x is the no. Of students interacted with the flu.

Q: Solve the differential equation (3xy+y2)+(x2+xy)y′=0 using the integrating factor μ(x, y) = (xy(2x +…

A: The differential equation is 3xy+y2+x2+xyy'=0.

Q: a differential equation is classified as a homogeneous DE if one can directly isolate all functions…

A: A differential equation is classified as a homogeneous DE if one can directly isolate all functions…

Q: Consider a first order differential equation. y(-x sinx + 2 cosx ) dx + x( 2 cosx)dy = 0 a) Find the…

A: Given , Differential equation is  y-xsinx+2cosxdx+x2cosxdy=0 Now ,we write the given equation of the…

Q: If y = f(x) is a function satisfies the differential equation f'(x)x³ + f(x)3x² = x³ ,where C…

A: We have to solve the given differential equation and find f(x).

Q: Find the general solution of the first-order linear differential equation xy′ + y = x2 ln x for x…

A: The first-order linear differential equation ,  xy'+y=x2lnxfor x>0. Solve the equation for the…

Q: Using Euler's method, compute y (0-5) for differential equation =y -x, with y =1 when x=0

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Q: y" - y = e2* - sin x

A: The given question has been solved in detail

Q: Determine the value of C for the given first order differential equation when x-2 and y=1. e#+v/ =…

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Q: Use separation of variables to find the general solution of the differential equation. y- dx 4…

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Q: Show that f(x, y) = e2x cos(x + In y) satisfies the differential equation 2f - yfyx = 5f.

A: Given that fx,y=e2xcosx+lnyShow that 2fx-yfyx=5f

Q: Obtain the differential equation associated with the given non-derivative equation in x and y. y =…

A: Given that obtain the differential equation associated with the given non-derivative equation in x…

Q: The integrating factor of non-exact differential equation (x°y³ – ®)dx – (y6 – x³y)dy = 0 - -

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Q: 38. Determine the integrating factor of the linear differential equation y' - (1 + tanx)y = e cos'x.…

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Q: x*y' = -x³y – csc (xy)

A: Given- x4y'=-x3y-cscxy To Find- The general solution of the above differential equation.

Q: Find the general solution of the first-order differential equation                       y cos x −…

A: Given: y-1cosx+dydx=0 for finding solution of given differential equation, we use variable separable…

Q: Without using an Integrating Factor, determine the particular solution of the given differential…

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Q: Consider the nonhomogeneous second order differential equation a°y" – xy' + y = nT +0, x > 1.

A: First we have to find the general solution of the differential equation x2y''-xy'+y=xlnx where x≠0,…

Q: An integrating factor for the linear differential equation = x - is (Select the correct answer.) x2…

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Q: Use integration to find a general solution of the differential equation                      dy/dx =…

A: Given the differential equation is   dydx = 2x(4x2 + 1).   dy =  2x(4x2 + 1)  dx Integrating on the…

Q: The homogeneous linear differential equation of constant coefficients of lowest order possible for…

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Q: is there any homogeneous linear second order differential equation such that two functions e* and t²…

A: Given: The two functions and   is the solution of the second order differential equation

Q: Solve the differential equation: (y² + xy°)dx + (5y² – xy + y° sin y)dy = 0 by finding an…

A: here we have to find the solution of given differential equation. thesolution is following.

Q: The differential equation governing the decay of a certain radioactive substance through time is dq…

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Q: Verify that the function is a solution of the differential equation.…

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Q: Find the particular solution that satisfies the differential equation and initial condition. f"(x) x…

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

Q: 3x√y. For y is not

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Q: Define the term homogeneous first order ordinary differential equation.  Hence solve x2y' + xy = x2…

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Q: (x+1) +y=In x dz

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Estimation

A new framework of data analysis where the new statistical methods are used for interpreting the results and analyzing the data is known as estimation in statistics.