The particular solution of the differential equation y y- 2y = sin3x is: y(x) =Ce3x+Ce3O y(x)=Ce2x+cos 3x O y(x)=3C1cosx+3C2sinx o y(x) =C1cos3x+C2sin3x

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

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Q: 2. Solve Bernoulli differential equation of y' + xy = xy².

A: We need to solve the differential equation.

Q: Find general solutions of the differential equation     x(x+y)y'+y(3x+y)=0

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Q: Show that the differential equation  (2xy3 - 3y2 + 2xy2)dx + (3x2y2 - 6xy + 2x2y)dy = 0 is exact and…

A: To show that the differential equation  2xy3-3y2+2xy2dx+3x2y2-6xy+2x2ydy=0 is exact and to find its…

Q: What is the general solution to the differential equation (2x- 2y- 3)dx (2x*- 4y-2)dy?

A: We have to solve the given 1st order differential equation.

Q: 1. Given the differential equation: y" = sin(5x). Determine its general solution. A. 150y = cos(5x)…

A: Given differntial equation          y'''=sin 5xthen we have to find it's general solution…

Q: Find the particular solution of the differential equation 2xy′ − ln x2 = 0, x > 0 that satisfies…

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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: Find a general solution of the second-order nonhomogeneous differential equation y" - 2y' + y =…

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Q: Find general solutions of bernoulli differential equations.   yy' - xy^2 + x = 0

A: yy'-xy2+x=0A first order differential equation of form N(y).y'= M(x)yy'=xy2-x = x(y2-1)⇒    y…

Q: Find the particular solution of the first-order linear differential equation     y′ + (1/x)y = 0for…

A: y/+1xy=0 On simplification, we get ⇒dydx=-yx⇒dyy=-dxx Now integrating on both sides, we get…

Q: One solution of the differential equation y''+y'=0 is y=e^-x. A second linearly independent solution…

A: We will find out the required solution.

Q: A solution for the differential equation is y = eux A1 sin (vx) + A2 cos (vx), where m and n are…

A: We will find out the required values.

Q: 2. Solve the differential equation: (y² + xy°)dx + (5y² – xy+ y° sin y)dy = 0 by finding an…

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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. Show that the differential equation (1 – 2y + x In a)dx + (e2v – 2x)dy = 0 is exact and find its…

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Q: Using the method of undetermined coefficients, a particular solution of the differential equation y"…

A: Given differential equation is y''-y'-2y=2 e-x   Let the particular solution of this differential…

Q: Find general solutions of the differential equation      2x^2y-x^3y'=y^3

A: 2x2y-x3y'=y3 We need to find the general solutions 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: Find the particular solution of the first-order linear differential equation        y′ + y = 6ex…

A: y'+y=6ex Comparing with y'+Py=Q, we get P=1 & Q=6ex Now the integrating factor is, IF=e∫P dx=e∫1…

Q: Find the solution of the D.E whose solution is given as y = 2(x² – 1) + Ce-x2.

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Q: Obtain the particular solution of (3x2-2y2)y'=2xy; when x=0. y=-1

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Q: Solution of given differential equation at x = 2 is (1 – a²) – 2æy = x² - (Assume zero initial…

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Q: Find a homogeneous linear differential equation with constant coefficients whose general solution is…

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Q: Find the particular solution of the given differential equations. (x² + 2xy - 4y²)dx - (x² - 8xy -…

A: Given equation is (x2+2xy-4y2)dx-(x2-8xy-4y2)dy=0

Q: Find the general solution of the given differential equation 1 2 -y' + y = -x(secx)²y2 x2

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Q: If yy of a differential equation is ce2x + Cze3x + cze-3x, then W = (a) 0 (b) (c) 5e-* (d) e5x d O a…

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Q: Find general solutions of the differential equation    (x+2y)y'=y

A: Given differential equation is Convert it in linear differential equation by simplifying. This is…

Q: Solve the non-homogeneous differential equation of 6y"-y'-y=1-x-x?

A: Given differential equation is  6y"-y'-y=1-x-x2

Q: The solution of the first order linear differential equation y' + ycotx = cosx is O…

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Q: 2) (x²y³ + y)dx + (x³y² – x)dy = o

A: (x2y3+y)dx+(x3y2-x)dy=0 this is an exact equation  M(x, y)= x2y3+y N(x, y) = x3y2-x We will evaluate…

Q: Find the homogeneous differential equation whose general solution is y = 3cos(x) - e3x/2 -…

A: Given the solution of a homogeneous differential equation   y = 3cos(x) - e3x/2 - 4xsin(2x) Find the…

Q: Find the particular solution of the given differential equations. 2. (x² + 2xy - 4y²)dx - (x² - 8xy…

A: (x² + 2xy - 4y²)dx - (x² - 8xy - 4y²)dy = 0

Q: . Given the differential equation: y" = cos(5x). Determine its general solution. A. 125y = -cos(5x)+…

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Q: Find general solutions of the differential equation  x^3y'=x^2y-y^3

A: the given equation is x3y'=x2y-y3 divide the equation by x3 y'=1xy-1x3y3            ...... (1)…

Q: The solution of the differential equation by variable separable method dy (1+ y²) (3x² + 6) 5- is dx…

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Q: Find the general solution to the non-homogeneous differential equation. y" - 3y' = sin(3x)

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Q: Find the general solution of the first-order linear differential equation y′ + 3x2y = 6x2 for x >…

A: Given: The first-order linear differential equation: y'+3x2y=6x2 for x>0.

Q: Choose a solution for the differential equation y'' - y = x2ex + 5: e-x(1/6x3 - 1/4 x2 + 1/4x + 3)…

A: Given non- homogeneous differential equation,y''-y=x2ex+5  ...(1). Solving the homogeneous part:…

Q: The complementary solution for following differential equation d3x + 5 d2x +26 dt2 dx dt3 150х 600t…

A: In the question it is asked to calculate the complementary solution of the function given below.…

Q: The solution for the differential equation dy dx tan-¹x 1 1+x² (et - y is

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Q: Find general solutions of bernoulli differential equations.   y' + 2xy = -xy^4

A: The given Bernoulli differential equation is,

Q: Find general solutions of the differential equation  (x^2-y^2)y'=2xy

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Q: The solution of the differential equation by variable separable method dy 3 + y?) (3x² + 6) is_ dx…

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Q: The General solution of differential equation defined by: x2 y"-2x y'-4y=0 is defined by 1 y(x) = C,…

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Q: The solution to the differential equation -y x cos(3x) - is: Select one: cos(3x) + cx2 O 3x² sin(3x)…

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Q: The solution of the exact differential equation (ycosx + 2xe") + (sinx + x²ev – 1)y' = 0 is:

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Q: The General solution of the differential equation 3x2 + 2x + 6 is x3 + x2 + 6x dy using variable…

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

A: The solution is given as

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.