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

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: It is known that h1(t)=e3t2, h2(t)=30e3t2 are solutions of the differential equation 4h" - 12h' + bh…

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Q: 4. What is the differential equation of the given functions? • y = Ce-* + Cze-2x + x y = Ce2* +…

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Q: The dependent variable y is missing in the given differential equation. Proceed as in Example 1 and…

A: To solve this differential equation, substitute y'=u

Q: 5.Find the general solution of the differential equation y'=x-y+3/x-y

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Q: 2. In the differential equation 4(3x+ y-2)dx-(3x+ y)dy =0, we let

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Q: 1. Consider the problem y' = 1 – 2xy, y (0) = 0. (a) Since the differential equation is linear, an…

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Q: 2 4 Solve the differential equation y dx - 2(y - x) dy = 0. If y = 1 when x = 3, determine x when y…

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Q: 2. Find the general solution of the given higher-order differential equation y(4) + y" + y" = 0.

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Q: When solving the nonhomogeneous differential equation y" - 4y' + 4y = x by undetermined coefficients…

A: To solve the following problem

Q: 1. Solve the differential equation: xy' – y = 2x In x

A: Use linear differential equation concept

Q: 2. Solve the differential equation (3x2 – x³ + 3y – 3.ry – y°)d.x + 3(x + y²)dy= 0, - -

A: Disclaimer: Since, you have requested for a handwritten solution and currently we are not providing…

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

A:

Q: 3. If the general solution to a second-order differential equation is given by cie + ce-5, find the…

A: In the question it is asked to solve the differential equations with initial values given.

Q: 1. Determine the solution of the differential equation y' - yx = -x given that y (0)=X

A: Part 2 number 1 To solve: The differential equation is y'-yx=-x,y0=X Calculation: Solve the…

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: 4. Find the general solution to the differential equation y²y" = y/ (where y' = )

A: To find solution of the differential equation: y2y''=y'

Q: show that there exists a unique solution to the differential equation y'=ln(xy); y(2)=1  the…

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Q: 4.Determine if the given function is a solution of the given differential equation

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Q: (9) Show that the solution of the differential equation y + y = -6ye» with y(0) = -1 is (e* –…

A:

Q: 2. The differential equation (4x'y'-6x'y-2r-3)dr +(2x*y-2x' ty = 0 is exact because aN

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Q: 5. Find the general solution to the differential equation et y" – 2y' + y 1+ x2 (where y' = )

A: Let us consider the differential equation y''+py'+q=g(x) To solve the equation  Determine the…

Q: II. dy dx 2x² x(y² + 1)

A: We have to find the best way to solve the given First Order Differential Equation by Finding…

Q: What is the solution of the first order differential equation y(k + 1) = y(k) + 5.

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Q: 7. In the differential equation 4(3x+ y-2)dx-(3x+ y)dy = 0, we let the substitution dw =

A: the differential equation 4(3x+y-2)dx-(3x + y)dy=0, we let the substitution dw=??

Q: If 2x3+3ycos(xy)+(cx2y2+3xcos(xy))y'=0 is the exact differential equation then c =?

A: The exact differential equation is defined as the differential equation of the form Mx,ydx+Nx,ydy=0,…

Q: 1. Choose a solution to the differential equation y" - y = x²e² + 5.

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Q: 2. A population is modeled by the differential equation: *= 3N (1-) (1-) dt 50, where N(t) is the…

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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: 1. What can you say about a solution of the equation y' = 49y² just by looking at the differential…

A: Given that : y' = 49y2. This is a differential equation and we find solution of this differential…

Q: 3x y"+y= e¯x2 - 4x + 2x² + e³x 8-12x - 10x²

A: Let us consider the given differential equation y''+ay'+by=Q(x) To solve the differential equation…

Q: 1. Obtain the differential equation associated with y=Ax2+Bx+C

A:

Q: What is the general solution of the differential equation; y’ = 2x cos (x^2)

A: solution:-y'=2x cosx2solving the differential equation we getdydx=2x cosx2y=∫2x cosx2 dxlet x2=t2x…

Q: 9. What is the particular solution of the linear differential equation ,3 Y = x° – 2xy; when x = 1,…

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Q: Find the general or Special Solution to the differential equation 2 y = (x-y₁²

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Q: 3. Show that the differential equation zxy

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Q: 4. If the characteristic equation of the differential equation y"+2y'-3y =0 is m² + 2m –3 =0, then…

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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: What is the degree and order of the differential equation (y") + (y")° + (y')' + 8 = 0 O degree 3…

A: (y''')4+(y'')6+(y')7+8=0

Q: 18. The solution of the differential equation 2xy = x² + 3y² when y(1) = 3 is dx

A:

Q: 8 Find the general solution of the differential equation: xy' + y: X Use lower case c for constant…

A: Given : xy'+y=8x+9x Following formulas are used- ∫1xdx=lnx∫xndx=xn+1  n+1

Q: 1.. The differential equation (3x² + 2.xy + 4y²)

A:

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

A: ## Given differential equation       f(y)d(y) = g(x)d(x)

Q: 3. ([3]) Suppose that a large mixing tank initially holds 400 gallons of water in which 50 pounds of…

A: This is a problem of IVP.

Q: 8- The solution of differential equation y" + 4y = 0 is.

A: Since the student has posted multiple questions and does not mention any specific question, so we…

Q: dyy3 1. Find solution of the differential equation;+2=- dr 2 2 ,with y(0) -2

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Q: Suppose that a large mixing tank initially holds 300 gallons of water in which 50 pounds of salt…

A:

Q: The differential equation y'=xy² is subject to the initial condition y(2) = 1. Find the value of…

A: Given,         The differential equation y'=xy2 is subject to the initial condition y2=1.

Q: What is the solution to the equation for the differential equation x^(2)y''+3xy'+y=0

A: The given problem is to solve the given differential equation , the given differential equation is…

Q: 2. | Determine the general solution of the given differential equation y" -6y" = 3- cos x

A: The solution is given as