se the substitution u(x,t)=X(x)T(t) and separation of variables to solve the partial differential equation utt=ux No boundary conditions are given. Take the separation constant as -a . Use the same methods used to determine the general solution to the heat equation as demonstrated in your notes and determine the most general solution in terms of a.

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Q: dy dt 3 + ty = 1+t, y(2₂) = 0 Solve this ordinary Differential Equation please

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Q: Use the "mixed partials" check to see if the following differential equation is exact. f it is exact…

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Q: - Solve the following partial differential equations X) = 30,T(t,0) = 50, T(t,1)

A: The partial differential equation given is as follows: ∂T∂t=α∂2T∂x2 with α=0.5. The PDE will be as…

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Q: Given a second-order ODE, y = y + xex: dx² (a) Identify the complementary function, ye for the…

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Q: = -y(2-y). Draw a direction field for the differential equation y Based on the direction field,…

A: given differential equation y'=-y(2-y)

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Q: homogeneous solution to the second order constant coefficient ODE’s. Solution must be real.

A: d3dx3y-3d2dx2y+3ddxy-y=0 A linear homogeneous ODE with constant coefficients has the form of…

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A: Differentiating with respect to x, we get

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Q: Use the "mixed partials" check to see if the following differential equation is exact. If it is…

A: Please find attachment below

Q: The function u depends on two independent variables: u= u(x, t). Find the general solution of the…

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Q: Identify whether the following differential equations are homogeneous or not. (a) (3x² – y²)dx+(xy…

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Q: 1. Solve the following first-order partial differential equation using the method of…

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A: Given               r=12, V1​=20, V2​=10⇒k1​=V1​r​=2012​=53​k2​=V2​r​=1012​=56​     The given system…

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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.