We will solve the heat equation u = 2 uzz, 0 < < 6, t> 0 with boundary/initial conditions: u(0, t) = 0, u(6, t) = 0, 2, 0<<3 0, 3

Q: Determine whether the process ~ X(t) = cos(wt); where w wide-sense stationary or not U(0, 1), is

A: According to the question,

Q: (a) F(x, y,z)= 3x²y -2z'x+y'. (i) Find VF. (ii) Find the directional derivative F(x,y,z) at the…

A: See the solution in the given fig.

Q: 3. y" +2y' + y = 2 sin t H(t – n), y(0) = 1, y'(0) = 0 A y(t) = (t+1)e-[cost+ (t+1-)e™-']H(t–n) %3D

A: The given differential equation is: y''+2y'+y=2 sin(t) H(t-π) ;              y(0)=1,   y'(0)=0

Q: Solve 3rd order ODE with forward and backward eulers method. from t = 0 to 0.1, h = 0.1, y0) = y(0)…

A: The third order equation is d3ydt3-2y=0. Consider dydt=p, d2ydt2=q⇒p'=q, q'=2y By Forward Euler…

Q: 35. Y"(t) +Y(t) = 8 cos t, Y(0) = 1, Y'(0) = -1. Ans. Y(t) 4 sint 4t cos t = cos t -

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Q: Show that the solution of the equation dx/dt=-x(k^2+x^2) With initial condition…

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Q: (3e^(x) sin(y)−9y)dx+(−9x+3e^(x) cos(y))dy=0 a) Considering that the equation has the form M (x, y)…

A: Using the rules for exactness or completeness of differential equation, it is obtained that equation…

Q: g- y" + 2y' + 5y= 2u(t) where: y(0)= y'(0)= 0, u(t) = a*e-bt {a and b are constants} %3D

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Q: 6) y" + 2y' = 8(t – 1); y(0) = 0, y'(0) = 1 %3D

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Q: 4: A:Find the solution of the initial value problem (d^2 y)/(dx^2 )+5 dy/dx+6y=0□( ) y(0)=2, And…

A: Given A. d2ydx2+5dydx+6y=0  ;  y0=2 and dydx=0 B. 2yz-3lnz=2x+5y

Q: Find y(2) and yG) For fundion yft) that saticFies initial-valve dy +2 dy +y dt =2+ (t-3) 6 Ult-3) ;…

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Q: dy/dt^2 – 4dy/dt – 5y =0, y(1) =0 ; y’(1) =2

A: Given differential equation d2ydt2-4dydt-5y=0  , y(1)=0 and y'(1)=2

Q: Find a particular solution of the equation y2y' = cosx satisfying the initial condition y(0) = 0.…

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Q: au at a²u 28. Solve Əx² U(x, 0) = 3 sin 2+x, U(0, t) = 0, U(1, t) = 0. = where 0 0 together with…

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Q: Find the solution of: y" +y = 2e' ,y(0) = 0, y'(0) = 0 Select one: a. y = sint – 2cost + e' O b. y =…

A: Using Laplace transform to find solution of Differential Equation.

Q: Use the method of undetermined coeffivients to find a particular solution to the non-homogeneous…

A: Differential equation is a equation that relates the variable with their respective derivatives.…

Q: Let u = (x,t) represent the temperature of a hose with length L. The temperature with t= 0 is u(x,0)…

A: To solve following PDE using method of separation of variables :      ut=α2uxx ,  0&lt;x&lt;L,…

Q: If y = Σ∞n=0 Cnxn, y' = Σ∞n=1 Cnnxn-1, y" = Σ∞n=2 Cnn(n-1)xn-2, find (x2 + 4)y" + 2xy' - 12y = 0 and…

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Q: 2. Explain why the system f x' {y'. 9 1 + f² + g² 1 + f² + g² trajectories as x' = f(x, y). y' =…

A: The given system of differential equations is: x'=f1+f2+g2y'=g1+f2+g2 The objective of the question…

Q: A 4-pound weight is hung on a spring and stretches it 1 foot. The mass spring system is then put…

A: Draw the figure, which is given below. In equilibrium,  mg−kx0=0⇒mg=kx0 Given, mg=4 and x0=1…

Q: a) Calculate the steady-state concentration of perfume particles. b) Formulate the initial-boundary…

A: Given Data: Let us consider the given data, ∂u∂t=∂2u∂x2u0,t =20 , u30,t=50, t&gt;0ux,0=60-2x ,…

Q: Now consider the case when the parameter varies slowly in time , that is consider the system…

A: The two equation in dynamical system which varies with time is…

Q: Use Variation of Parameters to find a particular solution to the non-homogeneous equation y′′−2y′+y=…

A:

Q: What is the particular eq. of the given:   y"-3y'+2y= xe^x +1

A: NOTE: Refresh your page if you can't see any equations. . for the homogeneous system, the auxiliary…

Q: Solve au_a²u əx² Ət __U(x,0) = = " 0 0, subject to the conditions U(0,t) = U(6,t) = 0, Interpret…

A: Using crank Nicolson method to calculate the numerical solution for ∂U∂t=∂2U∂x2  , 0&lt;x&lt;6,…

Q: Suppose that a projectile is fired straight upward from the surface of the earth with initial…

A: velocity v = rate of change of displacement y Hence, v = dy/dt Hence, d2y/dt2 = dv/dt = (dv/dy) x…

Q: n cos (n) Determine if the series converges or diverges. 4+n3 7 = 1 The given series diverges. The…

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Q: Suppose that the temperature in a given region is given by T(x,y)=200xy(1-x2-2y2) . Suppose that you…

A: Given that,Temperature in a given region is given byTx, y=200xy1-x2-2y2You and your friend are at…

Q: y=Ax+Cx^B is the general solution of the first- order homogeneous DEQ: (x-y) dx - 5x dy = 0.…

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Q: y' + 2y = 26sin3t, y(0) = 3 Laplace Tranform to solve for IVP

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Q: Let u(x,t)=e^(iwx).v(t)  and v(0)=1 be the solution of partial differentail equation      u_t=…

A: Since given that  u(x,t) =eiωxv(t) is solution of the partial differntial equation…

Q: Show that (0, 0) is an unstable critical point for the following system: 2xy + x3, 1 -x2 + y°. de dy…

A: We will find Jacobian matrix  for system of differential equation Then depend on eigen values of…

Q: Let u(x, t) = e^(iwx). v(t) and v(0 = 1 be the solution of part differentail equation u_t=u_xxxSo,…

A: Since given that  u(x,t) =eiωxv(t) is solution of the partial differntial 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.