The eigenfunctions of the BVP U =4 uxxi 00 u,(0, t) = 0 u,(1, t) = 0 are a. X,(x)= cos (n TIX); n=1, 2, .... o b. X,(x)= cos (n TtX); n=0, 1, 2, ... %3D С. "X,(x)=cos (x); n=0, 1, 2, .... 2n +1 - TTX); n=0, 1, 2, ... d. X,(x) = sin(- %3D e. X,(x)= sin (n TIX); n=1, 2, .... %3D

Q: XXXX 4. Show that the difference of two solutions of an inhomogeneous linear equation Lu = g with…

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Q: Solve the partial differential differential by separation of variables 70z + 6 = 0.

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Q: (x*D}-2xy0,D, +yo;-xD,+3yD,)z=0

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Q: Lu = V1+.x2 (cos y)ux + Uyxy – [arctan(x/y)]u x² уху

A: #Answer of 2(e)

Q: What is the Laplace Transform of e^3t?

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Q: 4. Let f and g two arbitrary real valued functions. A general solution of (F) is: a) u(r, y) = f(y –…

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Q: (1+x²) uz + Uy = 0, u(1, y) = sec y

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Q: differential equations dy /dt-2ty=0

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Q: Find the equation of the system of surfaces which cut orthogonally the system of surfaces x? = 10y?…

A: The objective is to find the equation of system of curves which cut orthogonally the system of…

Q: dy - 2y = 0, x(0) = 4, y(0) = 0 dt dx --x - 2y = 16te', 2x – dt

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Q: What is the length of EF? y 4 8 units 10- 7 units 4 2 units -10 -8 -6 4 10x -2- 6 units -4- -6 -8

A: solution of the given problem is below ...

Q: What is the Laplace Transform of t^4?

A: we have to find laplace transform of t4

Q: ifferential Equations

A: The given question is taken from the differential equation in which we have to find the solution of…

Q: f(x, y) = x*+ y* + 2 is a homogeneous function O TRUE O FALSE

A: We know that a function f(x,y) is homogeneous if  f(tx,ty)=t^nf(x,y)  is true for some integer n.

Q: Partial differential equations involve just two independent variables and partial derivatives. True…

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Q: y" + (3-d)y'-2(d-1)y-o: AIND a IF y(x) o AS x+0.

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Q: First order differential equations Determine the trajectories orthogonal to the curve family: x2 +…

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Q: dP 18 + 81P = 0 dt dt

A: Given differential equation is d2Pdt2-18dPdt+81P=0 Find the solution of the given differential…

Q: Shown below is the differential equations of an SIR epidemic model. Find a reaction network under…

A: Clearly we can see that S˙+I˙+R˙=-βSI+βSI-αI+αI=0⇒S˙+I˙+R˙=0⇒S+I+R=constant. (Integrating we get)…

Q: 3. Find the general solution of the partial differential equation *** (x" + y" )z ; m, ne IR* . ây

A: Find the general solution of the partial differential equation: xm∂z∂x+yn∂z∂y=x+yn+mxm+ynz ,  m,n∈ℝ+

Q: L-1 2s s2-10s+34) 34}

A: L-12ss2-10s+34

Q: Partial differential equations involve just two independent variables and partial derivatives.…

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Q: Use the method of separation of variables to solve 2.xyU, +2U¸ =0, U(x,0) = 3e4**

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Q: z = x² + x - 3xy + y3 - 5, find all points (x, y) wherein zand zy = 0.

A: The points are (1/4,1/2) and (1,1) the detailed solution is given below

Q: homogeneous differential equation of (x-y) (4x+y)dx + x(5x-y)dy=0

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Q: 2x²y =y" is sin x The differential equation X"y" O a. A second order partial differential equation.…

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Q: Day traders typically buy and sell stocks (or other investment instruments) during the trading day…

A: Let us start solving the problem step by step  A)We need to find possible collections  B)no of…

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.