4) Find ôw/ ôr if w= (x+y+z)*, x=r-s, y = cos(r+s), z = sin(r + s) the point (r,s)= (1,-1)

Q: dx 1)y /sec(3x) 2) y = Vu + 2u , x= u? - 3u

A: Definition used -            Chain rule of derivative -                             ddx(f(g(x))=…

Q: 1 - cos 2x if y = prove 1 + cos x y' = 2tanx.sec²x

A:

Q: 5) y"-y'-2y=x+cosx

A:

Q: 7- y" + 4y = cos x, y (0) = 0, y(n) = 0

A:

Q: dy B) Find for all the following dx 1) y = sin-13x 2) y = In(5x) 3) y = Vtanhx

A: Solution: As per our guideline we are supposed to answer only first three question please repost…

Q: [2x*dx (Ans. 3 2 x' +c ); (xi) J3x°dx - 3 In\x)| 3 |3x'dx (Ans. (Se* –x? +2)dx , (x + 0) (x) x' +c);…

A:

Q: y" +2y = 2x+5-e-2r y""-6y"=3-cosa

A: These questions are about ordinary differential equation.

Q: 3) у %3D 2u* + 1 x = 5u? – 5u -

A:

Q: 10. sec (10t) tan" (10t) dt 11. tan" (2w) sec" (2w) dw / cot (3r) csc® (32) dæ 12.

A: As per our guidelines, I can answer maximum one question. Since you have asked for three, So i did…

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: x³y' +3x?y" +xy' +8y=xInx Select one: a. YG.S +x(c2sin3lnx+c3cos3Inx)+x ( Inx -) - Inx: b.…

A: Given equation is  x3y'''+3x2y''+xy'+8y=xlnx            (i) Let x=et. Then…

Q: Hiw/ Find F'(x) 1. if F(x) = x, tanx 2-if y = Sinx it casx 3- Find g" ()if y co) = Sec y ex) g ex)…

A:

Q: find dy/dx y = | Vx V 1 5) 1+x 20) y=Cof"| 1-x, 15) y = \tan /2x + 7

A:

Q: Find the general solution of the system of equations 2 -5 x' 0 = - ( ² = ₂ ) x + ( cost), 0 < t < *.…

A:

Q: a) Use the Euler formula, e¹⁰ (cos(0) + i sin(0))" = cos(n) + i sin(n). b) Suppose y(t) = e-2t eit…

A: In this question, we will find the solution to the given problem.

Q: How did he get the value inside the circle f(x, y)=x² + sin(xy) Vf=x*+sin(xy)) i+ d(x²+sin(xy)), dx…

A: given ∇f(1,0)=2i+j we have to find the direction in which the directional derivative has some value.

Q: Hiw/ Find F'(x) 1 x, tanx if F(x) = X 2-if y= Sinx 3-Find y" (I)if yex) = Sec

A:

Q: What is the auxiliary equation for y"+by'+c=0, b & c is constant. What are the condition for this DE…

A:

Q: x' - x? = t, x(0) = -2, 0, 2; x(2) = 0; x(2.5) = -3, 0, 3 7. y'= sin(yx), y(0) = 0.5, 1,1.5, 2, 2.5…

A: We will use Mathematica to solve these. Each question has multiple initial value problems. 6 (a):…

Q: a3 f 2- Find the third derivative for for f (x, y) = sin əx3 -2sin?cos()+2 sin) sin By'sini )+2…

A: The given function isf(x, y)=sinxy

Q: DON'T USE CHATGPT Solve the following equation by canceling operator y"+y = 3x sin(x) (In the answer…

A: First of all we find the auxiliary equation for the corresponding homogenous equation. Find the…

Q: Differentiate: y = cos(5 e* ) e11 COS

A: Ans is. option a)

Q: dz If Z = x' sin(y), x = s²t³ and y = s°t2, %3D ds a) None of these b) 6st³ x² sin(y) – 3s²t²x³…

A: Given query is to find indicated derivative.

Q: Q2/ Find ow/or if w = (x+y+z)³, x=r-s, y = cos(rs), z = sin(r + s) at the point (r, s) = (0,1)

A:

Q: X₁. (x₁, Yr) (x', y') 0 (x, y) X x' = x + (x-x, )cos-(y-y,)sin y' = y, + (x-x) sin 0+(y-y,) cos P' =…

A: Solution:

Q: y= (12,4 + x)* + (1+)(Va² +x- c )cos²(4x), c)cos²(Ax), 3)4( 3 y = (12,4 +x)* + (1+x' Зx +x — с y = ?

A:

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

A:

Q: 2. y" +4y= sin2x + x2 using inverse operator method

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.