. 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: dx Xex+10, Complete the Square.

A: Given,          ∫1x2+6x+10dx

Q: Ea: Siny dydx

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

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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: 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: 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.