/hich of the following does not require the use of the dy nain rule to find ? dx A y = cos1 (10x – x²) - + 6y ,3 = x²y5 – 2 В 4x10 4 y = 10/x – + x5 x3 D sin(2x – y) + e²y + = 0 ||

Q: Suppose dy/dx = x- y and y = 2 when x = 1. Use Euler's Method with increments of Ax = -0.1 to %3D…

A:

Q: 4. (y? cos x - 3x²y - 2x) dx + (2y sin x - x³ + Iny) dy = 0, when x = 0, y = e %3D 5. (x2 - 1) dy =…

A:

Q: 3. (a) Determine f 2xe3*dx by using integration by parts. (b) Determine S cos(x²) 2x dx by using…

A:

Q: dy Find if y = In x5 + e-cos2x – In e?. dx dy 4 sin x cos x dy 5 es sin²x-cos2 x dx e cos2 x-sin? x…

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: the general solution of the DE (cosxcosy+2x)dx-(sinxsiny+2y)dy=0 is

A: The differential equation M (x, y) dx + N (x, y) dy = 0 is exact if and only if  ∂M∂y=∂N∂x.   The…

Q: 1 (5* )csch dy if Find dx 1. (а) y x>0. (ecosh 5x ) In Vx +1 d Show that for x 2 1, coshx- dx (cosh²…

A:

Q: Q1: A. Find of four of the following: dx 1. y = x sin-1 x +v1– x² 2. y = (x2 + 2x) tanh(x + 1) 3. y…

A: See the details solution in below

Q: Obtain the General Solution : • tan'ydy : sin xdx e • COS "x sinx dx o • (3t sinix) dx = sin 4x dy

A: Solve above differential equations.

Q: Find if y = In x5 + e¯cos2x – lIn e?. dx | dy_5, esin²x-cos²x 4 sinx cos x dy 5 %3D dx e cos²x-sin²x…

A:

Q: I. Find dy/dx of the following: 1. y= In 2x 2. y (In x) 3. y= In(tan x)

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

Q: 1/2 2. Approximate the integral: 1 - cos(2x) dx within an error of 0.01. x2

A: According to question given that∫0121-cos2xx2dx within an error of 0.01

Q: 1- Evaluate: 2y sinx dy dx อน 2- If u = x² + ey², x = sin 2t , y = cost² find Ət

A: Above question is solved.

Q: H.W.4 Find dy/dx for the following: 1) y= x+ sin x + sin 5x 2) y 32x + In (sin x) + In(sin 5x) 7) y…

A: Hey, since there are multiple questions posted, we will answer first question. If you want any…

Q: 3. Find a result by using homogenous for (x³ - 3x²y)dx- (x³y³)dy = 0

A: According to guidelines I have to provide answer only for  first qiestion...Thanks

Q: (1-1/2 x^2)cos x 3. y = 2cosxsin2x-sinxcos2x 4. y= x^3 - x^2cosx + 2xsinx + 2

A: Differentiation: 1.y=sinx2+cosxdydx=(2+cos x).cosx-sinx(-sinx)(2+cos…

Q: 4 2 1 Evaluate || - dy dx by reversing the order of the integration. O V Y +1

A: Given:∫04∫x21y3+1dydx

Q: 16 tan- dx 1 + x? dv 19. 20. (1 + v²)(1 + tan¬1 v) Oe® do 2e-0 sin 0 do 21. 22. e tal dx 2хe dx 23.…

A:

Q: 4. (y² cos x - 3x²y - 2x) dx + (2y sin x – x³ + Iny) dy = 0, when x = 0, y = e %3D

A: Note: According to our expert guidelines only one individual question is to be answered, kindly…

Q: 1. Find dy for the following functions : dx Vsin x.cos x 1+2.ln x 3y (ans.: coi x 2 tan x -)) x(1+2…

A: To solve given differentiation easily we take logarithm on both sides and then differentiate it.

Q: Bernoulli’s Equation xdy − ydx − xy^3dx − xy^3 ln xdx = 0

A:

Q: S2ta J 2tan x In (cos x) dx=

A:

Q: Given (1 + 3x sin y) dx - x² cos y dy=0 with y(1) = 0. Using Euler method with h=0.1, compute y'…

A:

Q: Q-3: Find the general indefinite integrals of: 1. S cos ntcos(sin(at)) dt 2. SVx +2x dx s dx 3-2x2-4…

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

Q: I. Find dy/dx of the following: 1. y= In 2x 2. y= (In.x) 3. y = In(tan.x)

A:

Q: Find the solution of the following IVP. * (yexy) dx + (xexy + sin(y))dy = 0, exy + cosy - 1 = 0 O…

A: The differential equation Mdx+Ndy=0 is said to be exact if ∂M∂y=∂N∂x. The solution is: ∫Mdx⏟Take y…

Q: 1- (x²1) + dy 2xy = 1 ty Cosx Ex Sinh 2- Sin(x) dy dx 3- - dy dx + 3x²y = x²x³ + 4- xlnx dy dy +y =…

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

Q: 10 a) Evaluate x cos(5x) dx by using integration by parts.

A: Given:

Q: I. Find dy/dx of the following: 4. y=√1+In²x 7. y In- COS X √4-3x² 5. y = sin²(In x) 8. y In, x- 6.…

A: Topic - Derivative of a function Power rule: ddxxn=nxn-1ddxln(x)=1x

Q: 1 The improper integral -dx is given by: x² +8x+41 Select one: O a. None of these sec-'((b+4)/5) de…

A:

Q: Н. W.4 Find dy/dx for the following : 1) y = x3 + sin x? + sin-1 5x 7) y = 3m (sec2x) eln(cos"*) 6…

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

Q: dy Find if y = ln x5 + e-cos 2x – In e?. dx dy 5 ,cos?x-sin2 x dy 5 4 sinx cos x = - dx e sin2x-cos2…

A:

Q: 1)Find dy/dx for following functions. 1) y = (In 4)* + In ( 1 + (Inx)2 + (In vx) 3 3x 2) y = tan-1…

A: Use formula of derivative  to solve

Q: Find the differential dy: y = sin(x√³). Ody = COS cos (T√²³) [2√T™- 2 O 0 O (E) None of these…

A: A detailed solution is given below.

Q: 1)Find dy/dx for following functions. 1) y = (In 4)* + In A + (In V) (Inx)2 2) y = tan (x*)

A:

Q: sin ® 3y cos3ydy cos 3y dy

A: We have to find out the integral

Q: 6) Find most general antiderivative of the fxn ) f(2) = secx (secx +tane) Secx +tanx, = secx COS X

A:

Q: 3. Find dy/dx of the followings: (а) у | V2 + cos³ t dt 2. •7x2 (Ъ) у V2 + cos³ t dt 2 (c) Y 1 dt t2…

A: using fundamental theorem of calculus part 1 ddx(∫abf(t)dt)=f(b)ddx(b)-f(a)ddx(a)

Q: Q2- Find for the following functions :- dx 1- y = (Inx)/tnx 2- y = x cos-1 x - v1-x² +sin-1x

A: We have to find dydx for the following functions... 1. y=lnx1lnx2. y=xcos-1x-1-x2+sin-1x

Q: find / sin³ x cos³ x dx cos³ 2x sinº 2x dx 11. 12. cos² x dx sin? x dx 13. 14. 16. 7 sin y dy 7 cos'…

A:

Q: Q2: - If y = 3sec3t and x = etan3t prove that: - dy (In3)2 + dx y 2logy x %3D

A: we have ,  y=3sec3t and x=etan3t we have to prove that , dydx=(ln3)2·yx·logyx…

Q: Find dy/dx for the following : 1) y = x + sin x² + stn-! 5x 2) y = 32x + In (stn x²) + In(sin-1 5x)…

A:

Q: (sın 2y - 2x cos 2y) dx +( 2x coS 2y + 2xsın 2y)dy=d when x= 2, Y = T 3. COS %3D

A:

Q: 7. Given y = sinh(e* +tan (2x)-cos (x+1). Consider | dy (i) et 1 dx 1+e2x 1+4x 1-(x+1) dy (ii) ex 1…

A: Note: - Since you have asked multiple questions, we will solve the first question for you. If you…

Q: n/3 CoSx dx dy, If we reverse the order of the following integral : cosx we get: Select one: siny dx…

A: The given function is  F(x)= cosx/ x

Q: 1. Defermine the integrating thators of the pallo wing non- exnet exact esuations. A. (1+ 4xy -…

A:

Q: 1) Find the indefinite integral S(3x* – 6vx + 3 cos x – 4e*)dx. 2) Find S 4(sin(6 sin x + x² + Vx))…

A:

Q: 4- Find dy/dx for y = 3(sin-(e-3x*)2 dy 31(sin-(e-3*")r* In3 2(sin-'(e-3x")- dx 1(-6х) е 1 - e-6x2

A:

Q: 6 The coefficient of sin( 2r) in the antiderivative of F(x): F(x) = (cos( is

A: We have to find the coefficient of sin 2x.

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.