In this problem we consider an equation in differential form M dx + N dy = 0. The equation (6x + 4x'y²) dx + (6x² - + 3)dy = 0 in differential form M dx + Ñ dy = 0 is not exact. Indeed, we have M, - N, = For this exercise we can find an integrating factor which is a function of y alone since M, - N, is a function of y alone. Namely we have (y) = Multiplying the original equation by the integrating factor we obtain a new equation M dx + N dy = 0 where M = N = Which is exact since M, N = are equal. This problem is exact. Therefore an implicit general solution can be written in the form F(x, y) = C where F(x, y) =

Q: Q3/ Solve the following equations: 1- х(2у — 3)dx + (x2 + 1)dy %3D0 dy 2- dx 4y x (у-3) 3. y' = 2xy…

A: Note that there are so many ways to write the final answer of the differential equation.

Q: he (4x' +6xy' )dx + (9x’y' +3)dy = 0 equation ² - 3x²y' +3y =e - Solve the so *+ 3x°y +3y=e -t…

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Q: a) 2xy dx+(1+x²)dy=0 b) y'+(4/x)y=x* ------by exact method ---by linear method

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Q: Show that the function f(t) = 1² – } is a solution of the dif- ferential equation (y')² – 4y = 2.

A: Given:       f(t)=t2−12.Differential equation is: (y')2−4y=2

Q: dy/dx= (6x^3-1)/(2xy-3x), y(1)= -1, x>0 Please show steps clearly, this is a seperable equation…

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Q: (xy^2- y^2+x-1)dx + (x^2y-2xy + x ^2+2y-2x+2)dy = 0 Start by using seperable equations.

A: given a differential equation,here need to solve this differential equation by seperation of the…

Q: Find the general solution of the D.E (y^2 – 2xy + 6x)dx – (x^2 – 2xy + 2)dy = 0 Show your solutions…

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Q: Find y' if x = y*. C Note: Leave your answer in terms of ï and y. y

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Q: Find the general solution of the D.E. (y^2 - 2xy + 6x) dx = (x^2 - 2xy + 2) dy = 0 Show your…

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Q: Find general solution of ODE   (x+y-1)dx-(x+y)dy=0 dy/dx = (x+2y-3)/(2x+y-3)

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Q: 3. (x - 1)dy - x?ydu = 0 4. (x2 - y2)dx + xydy = 0 5. (x2 - y)dx - (xdy – ydy) = 0

A: According to our guidelines we can answer only one question and rest can be reposted.

Q: Find general solution to Cauchy-Euler equation: (t^2)y''-2ty'-3y=t^2

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Q: mit equatio x²y' + 2xy + O with respect to x and solve for y'. Skip (you cannot come back) x²y + xy²…

A: Given query is to find the derivative.

Q: can you explain if this is true or false if y=x2+y2, then y'= 2x+2y

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Q: Find the value of a for which the equation y''+a^2y=0 has non trivial solution such that y(0)=y(pi)…

A: Since we have that                  y''+a2y=0                y(0)=y(π)   and y'(0)=y'(π) Then…

Q: Find general solution   y’’ + 2y’+ y = 2e^-t (t)^-2

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Q: Solve 24-4x²³/dx + xdy = 0 using the integrating factor M = 2² SPOXK

A: Solve 2(y - 4x2)dx +x dy=0, Using the integrating factor μ=e∫P(x) dx.

Q: Find a solution of x = y²_ (a) (0, 1) 1 1-xec y = (b) y = dy dx (0, 0) y = (c) (-1/2-1/2) (d) (2,…

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Q: Find an explicit solution for y′ = ye^−x^2 , y(0) = 1

A: The given differential equation is y'=ye-x2 and the initial condition is y(0)=1. Simplify the given…

Q: Find the general solution to this exact equation: y + (2ty-e^(-2y) ) dy/dt = 0

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Q: (2y² + 3x) dx + 2xydy = 0 Determine an appropriate integrating factor (x) or (y) that transforms the…

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Q: Find the general solution of the given DE 2xy^2 + 4 = 2(3-x^2y)y'

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Q: (xy^2 - x^3) + (yx^2 - y) y' = 0, y(0) = 1, solve for y when x = 2

A: Exact differential equation problems

Q: Please try find the general solution of problem y' + 3y = t + e ^ (- 2t)

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Q: Find the differential of the function y = In(S - 2x) 2dx dy = (5-2x) dy = (5 – 2x )dx -2 (5-2x)dx…

A: Given : The function y = ln(s - 2x).   To find the differential of the function y = ln(s - 2x).