. 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: 3. Consider the following helix with vector equation 7 (t) = 2 cos (t) 7 (t) 7 + tỉ + 2 sin (a)…

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

A: Given

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: dx Xex+10, Complete the Square.

A: Given,          ∫1x2+6x+10dx

Q: [ sec2t dt + S sin?t dt + § n'-1dt

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Q: Ea: Siny dydx

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Q: If y= sin f dt, then dy is dx 2x sin x sin x 2 VX sinx 2x sinx

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Q: Consider the wave equation 00, with (0,r) =(71) = 0, m(x,0) = sin x and -0 at -0. Then is

A: Given wave equation, ∂2u∂t2=3∂2u∂x2 , 0<x<π, t>0withu0,t=uπ,t=0andux,0=sin x, ∂u∂t=0 at t=0…

Q: The functions f,6) = ¼cos² #/½ sin %3D are Neither linearly dependent or А. independent B. Linearly…

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Q: Q1. Find by implicit differentiation; a) an equation of the normal to the astroid x/3 + y/3 – 4 at…

A: Note:- Since you have asked multiple question As per our policy, we will solve the first question…

Q: 19. Find y' in the parametric equations x =, t-1 t+1 A) (f – 1) 7-1 B) (1+ 1)? 2 +1 C) (1+1)? t +1…

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Q: Sit/ If r(t) = cos(t-1) i + sin (t-1) jitzo Does the particle have constant speed? If so, what is…

A: given position vector is

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

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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…

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Q: Compute the derivatives of the given functions. d. a) dt d [5 sin ¹5t = FI

A: As per the Bartleby guidelines, answering only first question as the other questions are not the sub…

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…

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Q: dy dy 2. Use the definition of the derivative dx and the product rule to find the de dy of the polar…

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Q: Q1) Solve the wave equation: at? ax? dU(x,0) Where: U(0,t) = U(1, t) = 0,- = 0,U(x,0) = 2(sinx+…

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Q: Solve the inhomogeneous wave equation on the real line Utt − c 2Uxx = sin x, x ∈ R U(x, 0) = 0,…

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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.