The diffeterctial equation is y²dx+ 3xZy² dx + dy=0

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: Find the particular solution that satisfies the initial condition: Differential equation: 2xy' - ln…

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Q: Find the general solution of the differential equation.

A: given,

Q: solve the for the general solution of the differential equation( linear homologous equation): (D2 +…

A: We have to solve the differential equation: D2+2D-1y=0 The given equation is in symbolic form where,…

Q: The particular solution to the nonhomogeneous differential equation y" + 4y' +5y = 10x + 3e-* %3D

A: The given differential equation y''+4y'+5=10x+3e-x. The particular integral is computed as follows,…

Q: Consider the differential equation: 1 y" – y = What is the general solution?

A: We have to find the general solution of the given problem.

Q: use the method of variation of parameters to determine the general solution of the given…

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Q: Show that the function  y1=x-1 is a special solution of the differential equation y'=1-(y-x+1)2 and…

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Q: Find the general solution of the first-order linear differential equation y′ + 3y = e3x for x >…

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Q: Find a linear differential equation with constant coefficients satisfied by e² ³x, and e4x

A: A linear differential equation having auxiliary roots m1, m2, m3,....... have following independent…

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: Find the general solution of the first-order linear differential equation y′ − y = 10

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Q: Determine the solution for the differential equation ry = In(x) for which Y(1)

A: y^2 = (ln x)^2  + 2 ln C

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: y' - y = 2x? 3

A: Given:   y' - 3xy = 2 x2   To Find: An explicit solution of the above differential equation by…

Q: Find the general solution of the given higher-order differential equation. du + + 6- drs dr4 12- dr2…

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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 general solutions of the differential equation    (x^2-1)y'+(x-1)y=1

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Q: The Equilibrium Value for the differential equation y = (y – 4)²(y) a are O 4,0 O 4 O -4,0 O 4, -4

A: To find the equilibrium value of y ' = (y - 4)2( y ) Equilibrium Value :  Is that value where f(y0)…

Q: y' = y + y3

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Q: The General solution of differential equation def ined by: 2x² y " – x y'+y=0 is defined by y(x) =…

A: Solving Cauchy Euler differential equation

Q: а) у +у — 1 y' +y = 1

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Q: y' = (4x + y)²

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Q: Obtain the general solution of the given differential equation using the appropriate method. y' = y…

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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 we use the method of variation of parameters, the particular solution of the following…

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Q: Consider the differential equation (y + 4)y' = gʻ-16). Is y = cx + 4 the GENERAL solution to this…

A: Simply solve the given differential equation and compare with the  given solution.

Q: Solve for the particular solution of the non-homogeneous differential equation. 1. y''+y=2x

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Q: (1 + x³) dy - x² y dx = 0, when x = 1, y = 2

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Q: If we use the method of variation of parameters, the particular solution of the following…

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Q: A solution for the differential equation is y = Pe-3x/2 + Qe–x/2, %3D

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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: Find the general solution of the differential equation. Use C, C1, C2,⋅ ⋅ ⋅to denote arbitrary…

A: Consider the given differential equation as v"x=5x2

Q: By the alimination of the arbitary constants a and b ,obtain the differential equation of which…

A: Given solution is xy=aex+be-x+x2 find DE by eliminating arbitrary constants

Q: y" – y' = e2" + e"

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Q: Find the general solution of the differential equation y – e³x+y = 0 using separation of variables.…

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Q: Find general solutions of the differential equation    (x+y)y'=1

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Q: is there any homogeneous linear second order differential equation such that two functions e* and t²…

A: Given: The two functions and   is the solution of the second order differential equation

Q: 3. Find the particular solution to the differential equation (y + 5)(x+2) if the %3D dx solution…

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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: Solve the differential equation for y= y(x) if y+2ry + 2x = 2 + 2y given the initial condition that

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Q: 3) Find the solution of the differential equation y = -ry + (/')².

A: The given differential equation is. y=-xy'+y'2                                .........1 This can be…

Q: Find the particular solution to the differential equation y′ = 4x + 3 passing through the point…

A: To find: y'=4x+3dydx-4x=3       dydx+Py=Qwhere P and Q are variables of x onlyI.F.(Integrating…

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

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Q: Find the general solution of differential equation, and when initial conditios are given, the…

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Q: Use the method of variation of parameters to find a particular solution of the differential…

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Q: Use separation of variables to find the general solution of the differential equation. e*(y' + + 3)…

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Q: Find the linear homogeneous differential equation with constant coefficients and the general…

A: Given the solution is y=2+3x-4x2e4x+e4x   NOTE: If Auxiliary equation of a differential equation…

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.