4.3 Find the solution subject to the following boundary and initial conditions of the wave equation, utt = a²uxx- Utt -4 4uxx = 0 (c)u(r,0) = 3 cos(2), u₂(x,0) = 1- cos(4x) u₂(0, t)=u₂(n, t) = 0 10≤x≤n,t> 0

Q: Find the solution to the VP 9y" +12 y' +4y =0 ; v(0)=-3 y'(0) =3 differential eq

A:

Q: Suppose A is a 2 by 3 matrix. Does Ax = 0 always have infinitely many solutions? Give a reason. Does…

A:

Q: If u = and , then what is the magnitude of 2 + . Round to the nearest hundredth. Answer:

A:

Q: dY 1 dt -1 a

A: This is a problem of stability Theory, a system of the differential equations.

Q: Find the solution of the IVP. y" + 3y' + 2y = 20 (sin t + 8 (t – 1)), y (0) = 1, y' (0) = –1

A: We solve the given initial value problem by using Laplace transform.

Q: (1) Show that the system x=-2 cos x - cos y y=-2 cos y - cos x is reversible but not conservative.…

A: To show that the system is reversible but not conservative.And to plot the phase portrait

Q: Draw approx. solution for the directional field for the first order with the initial condition y(0)…

A: Given directional field:

Q: Solve the initial value problem ut +2ux = -tu(x, t), t> 0, x R u(x, 0) = = sin x.

A:

Q: Find dy/dt. 11) y = (ecost/9)4 A) cos e4 cos(t/9) B) sin e3 cos(t/9) e4 cos(t/9) D) - (esin(/9)3

A: Use the chain rule of derivative and simplify.

Q: 2) Match equations a) y': 10. x-y and b) y' = -- with the direction fields (A) and (B). 1+x2 (A) (B)…

A: for differential equation second   This can be shown as the solution of a differential equation is…

Q: Let y=a,+a,t+a,t?+azt3+at4+ag+ag6+ d?y be the solution of .... .. ay +y=tan-lt ; у(0) %3D 1, у'(0) —…

A: Let us consider a differential equation L(D)y=f(x) Where L(D) is a linear differential function  Let…

Q: (19) Find the solution of the separable equations a) the general solution: b) the unique solution…

A:

Q: IfT: R² R³ is a linear transformation such that -n the standard matrix of Tis 13 T([2])-[3] . and T…

A:

Q: 4. Frame K' moves with velocity v in the x direction relative to frame S. The origins and axes of…

A: Introduction: The Lorentz transformation is a mathematical equation used in special relativity to…

Q: None

A: Step 1:Step 2:

Q: Consider the family of functions uc(x,t) of two variables x,t, indexed by the parameter c,…

A: Given partial differential equation or wave equation is 13∂2u∂x2 -8 ∂2u∂t2=0 -----(1) Also, given…

Q: (a) Solve the inhomogeneous 1st order equation Uz - Ut = cos t I U(x, 0) = 0.

A:

Q: Find the solution to ty'+ 2y = 4(t^2) with initial condition y(−1) = 2. and determine where the…

A:

Q: Let y=a, +a,t+azt² + azt³ + a4t* + aşt³ + agtº + ... d?y be the solution of dy +t- dt? +y=tan-t ;…

A:

Q: dy dy + 12y = 0, (y(t) is the position at time t) dt2 dt (i) Rewrite the given second order…

A: We have d2ydt2+dydt-12y=0(i) Let dydt=z⇒d2ydt2=dzdt         d2ydt2=-dydt+12ydydt=zdzdt=-z+12ythis is…