. Solve the following Wave Equation: a2u 4 ` əx² U(0,t) = U(, t) = 0 and %3D at2 au U(x,0) = 2sin x + sin 2x, (x,0) = 0 0

Q: Utt = 16urg u(0, t) = u(7, t) = 0 u(x, 0) = f(x) = sin(x) – 4 sin(3) u(x, 0) = g(x) = sin(2a) 0 0 t…

A: We will solve the given wave equation by variable separable method.  Let u(x,t)=X(x)T(t) is the…

Q: Find in the parametric equation d'y dx² x = 5 sin² t y = 2 cost 0≤t≤ 2π.

A:

Q: Find dy/dx and d^2y/dx^2.

A: Given

Q: (у) ну- (-см ) - уве Сай

A: Given differential equation is xy - dydx = y3e-x2

Q: Solve Ordinary Ditferential equatior: x) du + (g°cosyt 13 13e+ 4x sin 곳e 2.

A: Firstly expand the equation  (13ey +4x2sinx)dx+(y2cos y+13x2ex) dy=013ey dx+4x2sinx dx+y2cos y…

Q: Solve the wave equation using Fourier Transform: o'u ou - ∞ 0 %3D -12x utx, 0) = H(x)e u, (x, 0) =…

A:

Q: (b) Given that cos (t) Vos(21) sin' (t) Jos(2)" |cos(2t) dy Find for the parametric equation given…

A:

Q: 2. Consider the parametric curve r = t + 1, y = t - t. dy (a) Find d.r dy (b) Find da?

A:

Q: Hi, this is my question: Show that the following function is a solution to the wave equation…

A: The given function is u = sin(x-at)+ln(x+at).

Q: Q.No.3: a) Solve Cauchy-Euler equation d'y 3x3 dx3 d'y + 9x2 + 6x dx2 dy 6y = 1+ x3 dx -

A:

Q: (D² – 2D- 3)y = 2sin x a. y, = -cosx – 2 sinx =csx COSX b. y, = --cosx - - sinx COSX c. Y; = - cosx…

A:

Q: Question 3. Find the work done by the force fie ld F = xyi+y 2j in moving a particle along the curve…

A:

Q: The second order homogeneous Cauchy-Euler equation defined by: 2d²y +bx- dy ォマ +cy=0 dx2 dx (ay"…

A: We have to choose the correct answer

Q: 4. Find the parametric equation of the tangent line to r(t) = 4costi – 3tj %3D at Po(2, –n)

A: Given: To find the parametric equation of the given tangent line as follows, r(t) = 4 costi- 3tj…

Q: 6. Find * : y- + 5)ao TK, (b) y = Sin 5x I+cos 5x dx

A: Solving the problem by finding the derivative.

Q: Obtain the gradient to a curve with the parametric equations given by I = In - and y = sinh 2t whent…

A:

Q: dy (ii) Find dx? for the parametric equations x = t+ sin t, y= 1+cost

A: • This problem can be solved by using Chain rule as explained in step 2.

Q: Which of the following equations is NOT an exact equation? dy=0 B (xy - cos x)dx + (x² – 1)dy=0 (2x…

A:

Q: ignments: Find a solution for the following equations in two different ways: analytically and…

A: As per our guidelines we are supposed to answer only one question. Kindly repost other question as…

Q: (ii) Find for the parametric equations dx2 dy x =t – sint, y = 1 – cost

A:

Q: he equation dy dx (r,0) econd derivative is r = 60, = f'(0) sin 0 + f(0) cos 0 f'(0) cos 0 -f(0) sin…

A:

Q: [x(t) = 3t² – 3 v(t) = 2t +1 Find the slope of the tangent to the parametric equations at t=1.

A:

Q: n=2 (Inn)² n³ 3

A:

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.