Let f (x²) be a differentiable function. Which of the following function is the integrating factor 1 = 1(x) of the differential equation dx + 2f(x²)dy = 0 ?

Q: Find the differential equation of (y cos x + 2xe^y )dx + (sin x + x²e^y) dy =0

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Q: Find the differential equation such that y(x) = c,(x– 1) 2+czln(x – 1)(x– 1)

A: we will eliminate the variables by differentiating

Q: Find the integrating factor of a non-exact differential equation 6xy dx + (4y + 9x²) dy = 0.

A: As per the policy of bartleby, the provisions is to solve only one question at a time. So I am…

Q: Assume that the rate of change of y is proportional to y. Solve the resulting differential equation…

A:

Q: Find the integrating factor of the non-exact differential equation: dy= (e2x+y-1) dx

A: Given differential equation is dy=e2x+y-1dx which can also be written as e2x+y-1dx-dy=0 Comparing…

Q: Determine whether the following statement is true or false, and explain why.

A: For a differential equation of the form dydx+P(x)y=Q(x), the integrating factor is given by the…

Q: 5. Cx sin y +x²y = Ay

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Q: Find the general solution to the given differential equation. (Use C for the constant of…

A: To determine the general solution of the differential equation.

Q: What is the differential equation obtained by eliminating the parameter A from the relation…

A: The explanation of answer as follows

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

A: We have to verify that given function y=x lnx-4x is the solution of differential equation: x+y-xy'=0…

Q: Determine if the given differential equation is homogenous. (x³y³+1)dx + x⁴y²dy =0

A: Given differential equation (x³y³+1)dx + x⁴y²dy =0 Now we will check whether the given differential…

Q: What is the particular solution to the differential equation dx 1 + y = 2e-* with y = 1, dy -1 when…

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Q: Find the general solution to the given differential equation. (Use C for the constant of…

A: The given differential equation is dydx=x3y. Solve as follows. dydx=x3yydy=x3dx

Q: The Bernoulli's form of the differential equation x³ydx + (3x¹ − y³ )dy = 0 is

A:

Q: Assume that the rate of change in y is proportional to y. Solve the resulting differential equation…

A: Given  dydx=ky Points on the curve 3, 3 and 4, 6

Q: Let y=A cos x + B sinx is the solution of the differential equation

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Q: Find a differential equation by eliminating the arbitrary constants A, B from the relation y= Ae²* +…

A: (a) The given relation is: y=Ae2x+Bxe2x...(1) To find a differential equation by eliminating the…

Q: Find the linear differential equation of the bernoulli’s equation dy/dx-y[1/(2x)]-y^5=0 using dv/dx.

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Q: Find the general solution of the differential equation. Use C, C1, C2,⋅ ⋅ ⋅to denote arbitrary…

A: Consider the given differential equation: y'x=4tan2x-3cosx Here, the objective is to find the…

Q: If the function y = A sin z + B cos a satisfies the differential equation y" + y – 2y = sin z for…

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Q: dy -2 sin x where y (5 = JT dx

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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: Assume that y is a function of x and use the integrating factor method to solve the differential…

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Q: Find the differential equation by eliminating the arbitrary constant/s. Gedr cos x + Cge y = c1e 3x…

A:

Q: (a) Solve the first order linear ordinary differential equation dy x sin x- + (sin x + x cos x) y =…

A: The solution is given as

Q: The Bernoulli's form of the differential equation xdy - [y + xy³ (1 + ln x)]dx = 0 is

A:

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: B.Verify if a given function is a solution to a differential equation. 1 d²y dy 1x². +x=y= ln x dx²…

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Q: A function x(t) satisfies the differential equation dx –xª – 7x³ + 18x² - dt

A:

Q: For the given non exact differential equation, determine the integrating factor. (x2 + 2xy - y2) dx…

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Q: xydy - (y – 3x²) dx = 0

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Q: Find all solutions to the differential equation. Use c to denote an arbitrary constant. y' = x ln(x)…

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Q: Solve the first order differential equation. dy - y ln(y ecos x) dx = y sin xdx

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Q: Find the I.F of this nonexact differential equation dy/dx=1/(2xy)

A: Please see the answer below.

Q: Find the general implicit solution to the differential equation xy2 cos(x)dx + 2xy sin(x)dy = 0.

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Q: Find the Particular integral of the given differential equation d²y dx2 3x dx +5y sin(Inx) %3D

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Q: The Bernoulli's form of the differential equation x³ydx +(3x² - y³)dy=0 is

A: To determine the Bernoulli's form of the differential equation x3y dx+3x4-y3 dx=0.

Q: dy Vx ev+Vx dx

A: Given:        xdydx=ey+x

Q: dy +2xy = e-* is The integrating factor of the differential equation

A: By using linear differential equations integrating factory  we can calculate..

Q: Consider the following differential equation. (x2 + y2)y′ = y2 Let  f(x, y) =  y2/x2 + y2 .  Find…

A: This is a problem of differentiation of the function. Based on the general formula we will answer…

Q: Verify that y = (x³ – x) In cx satisfies the differential equation (x³ – x)y' – (3x² – 1)y = x5 –…

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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: Find the differential. Equation by eliminating the arbitrary constant  y = Ae2x + Be-2x

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Q: Use the initial condition to find the particular solution of the differential equation. Differential…

A: In this question, separate y terms in LHS and x terms in RHS and then integrate both sides to get…

Q: If tan x sin x is an integrating factor of the differential equation + Py = Q then P =? dx

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Q: Consider a differential equation y' = xy + xe -x

A: To solve a differential equation:

Q: Obtain the general solution of the given differential equation up to the form free from ln function.…

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Q: Find the general solution to the given differential equation. (Use C for the constant of…

A: Given,         dydx=x5y

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.