Suppose that y1 = e x and y2 = e −x are the solution of a homogenous linear differential equations. Explain why y1 = cosh x and y2 = sinh x are also solutions of the equation?

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: y + 3xy' – 2(y')³ = 0

A: Product rule of differentiation: (fg)'=fg'+gf' Chain rule of differentiation:…

Q: Find the general solution of the differential equation y" y 42y = -122t+84t². - - NOTE: Use t as the…

A: Given: The differential equation y''-y'-42y=-122t+84t2 To find the general solution of the given…

Q: Create a third order, non-linear Ordinary Differential Equation with enough initial values to be…

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Q: Find the general solution of the differential equation or state that the differential equation is…

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Q: Let y' (x) = V1– y²(x) be a differential equation. What is a solution?

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Q: Solve for the particular solution of the non-homogeneous differential equation. 1. y''=4

A: Solution :--

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

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Q: Find general solution of the Euler differential equation x2y” + 3xy’ - 3y = 0

A: x2y” + 3xy’ - 3y = 0

Q: is general solution of y = ae? x + be³x .8 differential equation اخترأحد الخیارات

A: Given: y=ae2x+be3x

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: 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: Now find the solution of the differential equation that satisfies the conditions y(0) = 4 and y' (0)…

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Q: 1 Verify if y = -+; xy + y = x² is a solution of a differential equation.

A: We have to verify the solution

Q: solve the for the general solution of the differential equation( linear homologous equation): y''-…

A: answer  Y = 9x22+ 3x detailed solution is given below

Q: Suppose the auxiliary equation of a homogeneous linear differential equation has roots m_1=-2 and…

A: We have given the root of the auxiliary equation which is m1=2 and m2=+-2i

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: 2x³y' = y(y² + 3x?)

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Q: x²y" - xy'+ 5y = 0

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Q: Find the solution to the Cauchy-Euler differential equation xy' +3y'+y=0.

A: The Cauchy-Euler differential equation of second order can be written in the form:…

Q: solve the for the general solution of the differential equation( linear homologous equation): y'' −…

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Q: y= 4 + Inx; xy'

A: Since you have posted multiple questions i can do first question as per our company guidelines…

Q: (D – 3D + 2) y = (1+ e-")?

A: I am attaching image so that you understand each and every step.

Q: - ydx + (x ++ Vxy )dy= 0

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Q: y' = (4x + y)²

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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: Find a homogeneous Euler-Cauchy differential equation whose general solution is Cx1+ C2x? where C,…

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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: Find a differential equation whose general solution is 9t = C₁e⁹t + c₂e-5t. y = = 0

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Q: Find the general solution of the differential equation: y" – 2y - 3y= - 3te. Fi: of the…

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Q: Find every nonzero solution of the differential equation y = y +2y°.

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Q: ylv – y" = 4x + 2xe-*

A: the

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

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Q: 5) Verify that y = 2e3 – 2x – 2 is a solution to the differential equation y' – 3y = 6x + 4. - -

A: Given that y=2e3x-2x-2    ......(1) Differentiating (1) with respect to x: y'=6e3x-2…

Q: Show that: a) The price of the stock itself, that is when u(t, X1) = X1, solves the…

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Q: x³y" + 3x?y" = 2x +1

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Q: Find the general solution of the differential equation or state that the differential equation is…

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Q: 3. (D² + 4)y = 0

A: Given:         D2+4y=0      Auxiliary equation is        m2+4=0         m2=-4          m=±-4…

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: Show that, if y, is a solution to a differential equation of the form y"+P(x)y' + Q(x)y = 0, then, a…

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Q: Find a differential equation whose general solution is -4t y = cjet + cze¬4.

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Q: Calculate the particular solution to the forced differential equation x" + 3x = 5cos(2t)

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Q: What is the particular solution of the differential equation y" + 2y" – 5y' – 6y = 5e?? Particular…

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Q: Show that y1 =- and y2 = Vx are solutions of the following differential equation 4x3у" + 7x?у' — ху…

A: According to the given information, it is required to show that the given y1 and y2 are the…

Q: (D² – 2D + 5) y = 25x² + 12

A: Given: D2-2D+5y=25x2+12 So,  The auxiliary equation is: m2-2m+5=0 Now solve; m2-2m+5=0m1,…

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.