Utt uxx; 00 u(0, t) = u(1, t) = 0; u(x, 0) = 0;u,(x,0) = 1 u(x.t) = 2(1-cosna) sin(nax) sin(nat) a. u(x,t) - f0).sin(nx)dx.sin(nx)sinnx b. u(x, t) - C. 2(-1)" u(x, t) sin(nnx).sin(nt) %3D d.

Q: Show that u(x, t) = 4 tan-1 I-ut ev where v is constant, is solution of Uxz – Utt = sin(u)

A: To check the given solution satisfy the given partial differential equation, substitute the solution…

Q: * Find dy/dx for the function y=2 sin(3x) cos2x 4 sin (3x) sin (2x) - 3 cos (2x) sin (2x) O 6 cos…

A: We know that derivatives  general power rule is - d(xn)/dx = nxn-1. And d(sinx)/dx = cosx ;…

Q: Find y' where y = tan(11a? + 8) v173 + 17 Answer: 51a2 y/ = sec2 (22æ)\/172³ + 17+ tan(11a² + 8)…

A: I have used the rule for composition of function and multiplication of functions

Q: Find y" in Exercises 71-78. 71. y - (1 + 2) 72. y - (1 - vī) 73. y - cot (3x – 1) 74. y - 9 tan 75.…

A: “Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: V ss Vst Vts Vtt || || 11 11 V sin(2s² - 4t²)

A:

Q: f'u where f(u) =ln(cos(g(2u)))

A: We have to find the derivative of given composition function

Q: fze [sin(3x)]-m(x, y, z), where m(x, y, z) = Part C. yz-1 %3D

A:

Q: i. y" - 4y + 5y = 39xe* sin(x) + 47e * sin(x)

A:

Q: 2. (5) Find f, for the function f(x, y) = sin (x + y²)

A: