Give a particular solution for y" – 2y' + y = 1+x2

Q: The differential equation (4x2y2 + 6x y )dx + (5x3y + 8x2)dy = 0  has an integrating factor of the…

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Q: x'y" – xy' = Inx

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Q: 5. Show that the differential equation y" +a²y = f(x), y(0) = y'(0) = 0, has 1 y(x) = -…

A: proof:-we have          y(x)=1a∫0xf(t)sina(x-t)dt   ⋯(i) differentiate by leibnitz's rule(i) , we…

Q: find general solution of following differential equations: y'tanx=2y-8,y(1/2pie)=0

A: Given differential equationy'tan x = 2y-8⇒ y' = 2ytan x- 8tanx         ∴ y' = dydx⇒ dydx - 2tan x. y…

Q: Find the solution of the differential equation that satisfies the given inital condition.…

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Q: from the partial differential equation by eliminating the arbitrary function z=(x2+y2+z2)

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Q: fx' = 9x + 7y ly' = 2x + 2y

A: We see that x'y'=9722xy. 9722The eigenvalues of A are the roots of the characteristic equation…

Q: (2) The particular solution y,(x) to the differential equation y" + 100y = sec2 (10x) is of the %3D…

A: Given y"+100y=Sec2(10x) ---1Compairing with y"+q(x)y'+r(x)y=g(x).Auxilliary equation corresponding…

Q: x³y"+xy'+4y = cos (2 ln x) bulunuz.

A: See the attachment

Q: x²(a+x) 2. Family of strophoids with the equation y² %3D a-x

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Q: 1 of these 2 differential equations: dx dy O and (2x sin y +y) dx + (x² cos y + x)dy = 0 What are…

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Q: Verify for a > 0, that y = is a solution of the nonlinear differential equation yyll = x.

A: The function is a rule that associates or fixes a number to the particular point x. If , then the…

Q: Determine the complete solution of the differential equation y" + 4y = 2cos2x %3D subject to…

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Q: 9. The characteristics of the partial differential equation *3 = 0 ду a əx dy +2- дх ду + cos? when…

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Q: Find the particular solution of the differential equation with the initial condition given below.…

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Q: 3. Find the general solution of differential eguation y" - v' - 6y = 0

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Q: Obtain the differential equation of all straight lines at a fixed distance p from the origin * O…

A: The general form of equation of a line which is at a constant distance c from the origin is…

Q: Obtain the particular solution of (3siny-5x)dx+2x^2cotydy=0 using Bernoulli's Equation. (Complete…

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Q: (a) Verify that 8x² - y? = c is a one-parameter family of solutions of the differential equation…

A: The differential equation ydydx=8x. We have to verify that 8x2-y2=c is a one-parameter family of…

Q: (y') ² + (x-2x^-½) y'+ x^-1 - x^½= 0

A: As per the company rule, we are supposed to solve one problem. Therefore kindly repost the second…

Q: y(4x + y) dx - 2(x² - y) dy = 0

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Q: Obtain the roots and the factored operator form linear differential equations y = x2 – 5 sin 3x y =…

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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: Use variation of parameters to find the general solution of the differential x²y" - 5xy' + 5y = 4x…

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Q: The integrating factor of the differential equation 2xy dx + (4y + 3x^2) dy = 0 is . Does not exist

A: Ist question was incomplete I have to do the second question Please repost ist question correctly

Q: Show that y is a solution of differential equation = 1-. dy %3D dx

A: y'(x)=1-yx We can simplify it as: dydx+yx=1First-order linear ordinary differential equation.…

Q: Verify that the indicated function is an explicit solution of the given differential equation.…

A: Calculation shown in the solution is correct , i am providing you the  answer for each boxes…

Q: Find the differential equation of the family of parabolas with vertex ar Focus on the x-axis * O y =…

A: We have to find

Q: Consider the differential equation y = x+ y. Use Euler's method with Ax = 0.1 to estimate y when x =…

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Q: The transversality condition holds for the partial differential equation X4x +Uy=0 with the initial…

A: In the given question we have to check the transversality  condition of the given P.D.E s.t xux+uy=0…

Q: 4.Calculate the differential equation y''= 3x + y2 + y + y', y (0) = 2, y (1) = 4 by shoot-ing /…

A: Given that the differential equation is  y''=3x+y2+y+y'; y(0)=2, y(1)=4 Also given that h=1/3 we…

Q: Determine the particular solution given the differential equations and conditions. 2= 3e* , y = 6…

A: dydx=3ex, find the particular solution and the function

Q: Solve for the solution of the given Partial Differential Equations with boundary conditions. Əri =…

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Q: Determine the particular solution of the given differential equation: y = 2(3x +y) – 1. when x-0.…

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Q: Match the differential equation with its direction field. y' = 5(x + y) – 1 -0.6- --0.4 - -0.2 0.2…

A: Given that y'=5x+y-1 Let fx, y=5x+y-1 then y'=f(x, y) As, we can see in given problem f(x, y)…

Q: xy' + 2y' + 2y O with initial condition y(0) = 1

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Q: 3] Form the partial differential equation by eliminating arbitrary function from z = e® f(x – y) -

A: Given: Z=exfx-y

Q: Select the function which is a solution of the differential equation. y" – 2y + 10y = 0 O y = 3e*…

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Q: (f). Verify if the differential equation given by 10x°y* + e¬Y + 3 sin(4x + 3y))y' + (6x²y° + 4…

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Q: dy 2. 2xy da 3. 2ydx + x (x² In y – 1)

A: We are asked to solve differential equations.

Q: Verify that the indicated function y = p(x) is an explicit solution of the given first-order…

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Q: The differential equation 3y(x -1dx+(x³ +8y– 3xdy = 0; is exact because OM ON %3D

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Q: Q.2 (a) Form Partial differential equation from z = ax² + by?

A: the given equation is z = ax2 + by2 .......(1)

Q: Form the partial differential equation by eliminating the arbitrary constants a and b from z = ď² x…

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Q: Find the particular solution of the differential equation (1-cos(2t))dy/dt=xsin(2t) given that…

A: The given differential equation is 1-cos2t dxdt=x sin2t     with xπ2=2. Solve as follows. 1-cos2t…

Q: Verify that the indicated function is an explicit solution of the given differential equation.…

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Q: Find the homogeneous linear differential equation whose solution is y=-e^(3x/2)-4x sin⁡2x.

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Q: Find the particular solution of the differential equation (2xy - sin x)dx + (x² - cos y)dy = 0, when…

A: Exact differential equations

Q: The differential equation (2x' - xy - 2y+3 dx- (x²y+2xdy = 0 is exact because OM ON

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