@ Sahe the wibrating hring problem. uco,E) = u(#,t)=0, u(x,o) = $in (2x) + sin (3x). Uelx,0) = sin(9x) - Ysin(10x), 0£xtT

Q: Find dy/dx in terms of z and y if cos² (3y) + sin² (3y) = y + 15. I

A:

Q: |x° (x³ + 2)³ dx 2)3 dx

A:

Q: 3) Find y" if y= 9 sin x.

A:

Q: fip xp COS T 2. Oa) 2x sin(x) cos(2x) P-sin(2x) d- sin(x)+2x Osin(x) acer

A: y=cos (x2) We need to find dydx

Q: 1 7. sin0 tan0 + cos0 = %3D cos0

A:

Q: dx x4+16 Įtan-( x2 + c 4

A: Given that, ∫xx4+16dx

Q: Use  DeMoivre’s theorem  ( Cos(x) + jSin(x))n = Cos(nx) + jSin(nx) to show that Sin3θ=3sinθ- 4…

A:

Q: Exam 1 Review • Find the Indefinite Integral 1. a) √ x²√³x²=4 dx → == S (2seco)² √√(2sec @)²-9…

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Q: Find ds/dt if 3t + 3s sin(3t) + 3cos(t) %3D

A:

Q: Generate a 3D plot based on the equation z=sin(x) +cos(y), both x and y range from 0 to 2 pi. Please…

A: [x,y]=meshgrid(0:2*pi); z=sin(x)+cos(y); surf(x,y,z)

Q: [17 sin³ x costx dx 5.

A: Given: I=∫17sin3xcos4x dx. To evaluate: Value of integral I.

Q: AN tan sec()dv A 2 2 2 14s 1YS

A: The given integral is,

Q: sin(3t)dt

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.