1. The equation d'x _ ô²x¸ ð°x dy dwy' əw = 3 has the dependent variable x and independent variables . 2. The highest derivative that a differential equation contains is called. 3. The differential equation 3xy" + 5y'y' + cos y = et* is not linear because of the term,

Q: 2. x²y' – 2xy = x* + 3; y = 2 when x = 1

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Q: Show that ¢(x) = Ce³* + 1 is a solution to dy/dx – 3y = -3 for any choice of the constant C. Thus,…

A: We have to check Q(x)=Ce3x+1 is solution of given differential equation.

Q: 2. What is the integrating factor of the differential equation (x² -y²)dx + (x² - 2xy)dy = 0?

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Q: Show that given differential equation dy y cos x + sin y + 9 – 0 is Exact and dx sin x + x cos y + x…

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Q: first-order

A: Given : y' = x9y + sin(x) The standard form of first order differential equation is  y' + p(x)*y =…

Q: (b) Form the differential equation by eliminating the arbitrary constants a,b from y = aez + be 8z

A: Differentiate twice with respect to x then we get the answer

Q: Find the general solution of the first-order linear differential equation. y + y = 16 cos (x)…

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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: Heat transfer from a body to its surroundings by radiation, based or he Stefan-Boltzmann law, is…

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Q: 9. From the differential equation sinh 2x, sketch some of the family of curves. %3D dx

A: Given differential equation, dydx=sinh(2x)dydx=e2x-e-2x2∫dy=∫e2x-e-2x2dxy=e2x+e-2x4+C

Q: Write down a first order differential equation for the current in an LR-circuit to which a voltage…

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Q: What is the solution to the differential equation 2 = 2xy satisfying the boundry condition y = e…

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Q: Suppose that y1 = e x and y2 = e −x are the solution of a homogenous linear differential…

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Q: What is of the differential equation (3 +y+ 2y sin² æ) dx + (x + 2xy – ysin2x) dy = 0 ? O 2x sin 2x…

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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: Find general solutions of the differential equation    (2xsinycosy)y'=4x^2+sin^2 y

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Q: [cos y + 1]dy + [tanx (siny + y)]dx = [sin y cos x + y cos x]°dx gettyimages When:x = 0;y=

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

A: See the attachment

Q: Suppose that x = 0 is a regular singular point of the differential equation 4xy" + 2y' + y = 0 Then,…

A: Given: x=0 is a regular singular point of differential equation 4xy''+2y'+y=0. To find: Indicial…

Q: 2. Form the differential equation from the circle passing through the origin having their centers on…

A: This question is based on forming differential equation by eliminating constant.

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: 5. Obtain the Differential Equation from the family of vertical parabolas whose vertex is at (h,k).

A: Formation of the differential equation

Q: The independent variable x is missing in the given differential equation. Proceed as in Example 2…

A: Given:y+8yιι =yι2   →1Let yι =u →Ad2ydx2=dydxd2ydx2=dudy=dydxd2ydx2= ududy →Busing Aand B in 1we…

Q: The differential equation dudx=5u+10  admits one equilbrium solution that is    asymptotically…

A: The given solution is  unstable whose plot is shown below.

Q: Find the differential equation of the family of cissoids: y^2 = x^3/ (a-x)

A: Perform the differentiation and eliminate the constant term in the differential equation to obtain…

Q: Find the particular solution to the differential equation: dy = 3x² cos² y. sSolution passes through…

A: Differential calculus is one of two main parts of calculus which is concerned with the study of…

Q: The given differential equation is already in standard form, as the coefficient of the highest order…

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Q: Consider the differential equation y' 2x - (A) At the point (- 1, 0.5), the direction field has a…

A: Given , differential equation y'=-2x. a. We need to calculate the slope at point (-1,0.5) Slope…

Q: 4 By using separable variable method, find the general solution of the differential equation dy _y…

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Q: Suppose dr - =4sin(2x) and y= -2 when *=. what is the particular solution to the given differential…

A: In this question, we need to find the particular solution to the given differential equation.

Q: Show that the differential equation dy -2 - yezy dr rezy – 2y is exact and find its solution. 3.

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Q: If m1, m2 are the real and equal roots of the auxilary equation of second order linear differential…

A: Let us consider the second order differential equation y''+py'+qy=0 To solve the differential…

Q: Suppose that x = 0 is a regular singular point of the differential equation x²y" – x(x + 3)y' + (x +…

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Q: If the family of curve has 3 arbitrary constants then the corresponding differential equation is

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Q: Show that y=x and yex are lenean inde pendent Solution of the Corres pondinp hamogeneous part ot the…

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Q: If the family of curve has 3 arbitrary constants then the corresponding differential equation is a)…

A: See solution below

Q: The differential equation formed by eliminating arbitrary constants a ,b andc: y = ax + bx + cx + 8…

A: In this question, we have to find the differential equation by eliminating parameters.

Q: Suppose sinh 2x, y2 = 6x, y3 = cos 2x are solutions of a linear homogeneous differential equation…

A: To find the differential equation :-

Q: What form of the particular solution is appropriate for the differential equationy'' - y'=4+4e*.

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Q: 2. Form the differential equation having y=(sin-x)²+ A(cos-lx)+B. where A and B are arbitrary…

A: Introduction :

Q: obtained in factored form a linear differential equation with real constant coefficients that…

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Q: 8. The differential equation (2x' -xy² -2y+3dx-(x'y+ 2x)dy =0 is exact because ON

A: Given:     Differential equation 2x3-xy2-2y+3dx-x2y+2xdy=0 The differential equation is exact if…

Q: What is the general solution with steps of the differential equation y’=sin(3x)y+y+sin(3x)+1

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Q: 13. Obtain the differential equation of the family of straight lines at a fixed distance p from

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Q: 5. In the differential equation 2rydx + (y² -xy-0. what is -- 心

A: Solution

Q: If the family of curve has 4 arbitrary constants then the corresponding differential equation is c)…

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Q: The given differential equation is already in standard form, as the coefficient of the highest order…

A: We have to find Wronskians.  Wronskian W(y1, y2) is the  W(y1, y2) = y1y2' − y2y1' Since y1 and y2…

Q: 4. Obtain the Differential Equation from the family of curves of the form y = xC

A: To form a differential equation from given family of curves. Differentiate given family of curves…

Q: Determine the solution of the differential equation y*y' = 4x² met die beginvoorwaarde dat with the…

A: As per our guideline,we are supposed to answer only one asked question.kindly repost other question.…