Given f(r, y) = sin(x + y) where a = s°t, y = 3s - 4t. Find f.(x(s, t), y(s, t)) = cos( st1+35 - 4t 42) (36241 + 3) %3D COS fi(x(s, t), y(s, t)) = cos( st1+35 - 4t)(4st3-4) x %3D Note: This question is looking for the answer to be only in terms of s and t

Q: Find f. f "(x) = 7 + cos(x), f(0) = -1, f(7x/2) = 0 %3D %3D f(x)

A: “Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Find f if ƒ"(t) = 2et + 3 sin(t), ƒ(0) = 2, ƒ(π) = 5. f(t) =

A: f''( t ) = 2et + 3sint f( 0 ) = 2 f( π ) = 5

Q: " + y = 12 cos 2x - sin x. A. " + y = sin 3x +4 cos x. A

A: Given: y''+y=12cos2x-sinx

Q: (a) fr = 4xz2, fy = yz and f; = xz 2 sin (x), fy = cos(x)y and f: = e" z z + y? If, f = = frâ + fyŷ…

A: a) Given f=fx+fy+fz and F→=fx x^+fy y^+fz z^ and  fx=4xz2, fy=yz, fz=xz So, we have f=fx+fy+fz…

Q: If 7'(t) = (cos t, e2t, 3t²) and r(0) = (3, 1, –2), find the function 7 (t).

A: Given. f'(t) = (cos t , e2t , 3t² ) To calculate the vector function are we need to integrate the…

Q: (c) y/" + 4y = 3r cos(2r)

A:

Q: If f(r) = cos sº COs sº ds then 82 f'(r) =|

A: We have to find the derivative of f(r)

Q: If = cos(2x), then y = __ dy dx O -cos 2 (2x) + C Osin 2 (2x) + C O-cos(2x) + C Osin(2x) + C ?

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.