5) [| dydx 6) y cos xy dxdy 00

Q: 3) Find dy dx a) y = x+In(sec 3x) %3D In(x+)

A: solution:-

Q: (a) (e* +In (y ))dx ++1 dy = +1 dy = 0 , y (In (2)) =1

A: note : as per our guidelines we are supposed to answer only one question. Kindly repost other…

Q: Prove that when y = e 2 Sin 2.x, then 4- d y dy +17y=0 +4. dx? dx

A:

Q: Let y = x. Find dy and Ay at a = 8 with dx = Ar = 1. dy Ay =

A:

Q: 20) Let y=7x+5x Then compute dy and Ay for X= -7 and dx =0.4. dy =? and Ay = ? Gounded 6o 4 decimal…

A: Derivative: - The derivative of the function is the equation that we find. The instantaneous rate of…

Q: af dy %3D Y Given f(x, y) = 17x² sin y then 17x2 cos y O -34x cos Y O -17x² cos Y 34x cos Y II

A: The function is given by fx,y = 17x2siny To evaluate : The expression of ∂f∂y

Q: dy evaluate dx (sinx+1) 5-1f: y = (cosr+1)

A:

Q: Q) Lind d/dx of ® xe 1o x+3J = 0 2 2sinx cos y =1 ® x -se cs

A:

Q: Find af af and f(x, y) = etry In(6y) af 4yln(6y)e^(4xy) af 1/ye^(4xy)+4xIn(6y)e^4xy dy f(x, y) = cos…

A: In the first part the answer is correct but you have mistakenly not taken bracket for 1/y . You can…

Q: dy dy +у сos x + 2xey — Зх2 %3D (1 — х?ey) dx sin x dx

A:

Q: dy at t= T is dx If x=t+sin 2t , y = 3t – cos 2t, then O a. -1 O b. 1 O C. -2 O d. 2

A:

Q: y=6 In(cos(e7")). dy AeBt sinC (e7 dt Then %3D cosº (e7) where A = %3D %3D D = BCD

A:

Q: ecsch(ry) + Tr° -cos(0)

A: Let's find.

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: (e* + In y +) dr + + In a + sin y) dy = 0

A: By Bartleby policy I have to solve only first one as these are unrelated problems.These are…

Q: Can you help me step by step?

A: According to the given information the given function is:

Q: y= A cos at a solution to y" + 3y = 0 such that y' (1) = 2? %3D

A:

Q: Evaluate sczxay) dx^ (x+ 3y) dy along the poth C: ure on y =1-3 from l0,)) to Cl,0)

A: Line integral problem......

Q: A. Find dy dx 9. sin y = In(x + y)

A:

Q: (Xy,Z)%3Dex(cosy +sinz) fr?, fy =?

A:

Q: Q1-If x= cot- VE, y =, find d²y dx' dx2 at t = 2.

A:

Q: sinxsinydx + coSXcosy dy = 0

A: Let us consider the differential equation f(x) dx=g(y) dy. This is the separable form of the…

Q: f SSR5e -27 sin(5x)y cos(2y) dxdy = f, 5e-2¹ sin(5x) dx f2, y cos(2y) dy where R = [-1, 1] x [1,2].…

A: This is a double integration problem

Q: Q1) Lind dy/dx of O xe 1o X +3y = 0 2 2sinx cosy=1 9 x = sec!

A: As per our company guidelines we are supposed to answer only one question kindly post other question…

Q: 7 xsiny dx + Cx²+1)cosy dy = 0, yC)=TT/2

A:

Q: nis is an exact DE. * 3x+ Qy? ) dx t (Axy t ly') dy = 0 O True O False

A:

Q: - (2y cosx + sin* x)dx : sin x dy, when x =y= 1 %3D

A:

Q: Let w = (sin(x) +7 cos(y)) dy ^ dz + (2³ – y cos(x)) dz A dæ + 14xyz da A dy. Find dw. dw = dx A dy…

A:

Q: dy Find dx for y = 14x +5 coS x. d(14x+5 cos x)%3D

A: Formulas:1. ddxxn = nxn-12. ddxcosx = -sinx

Q: -If x= cot- VE, y = ;, find dy dx'dx2 at t = 2.

A: We will use the formula (f(g(x))' = f'(g(x))g'(x)uv' = vu'-uv'v2 Given x = cot-1ty = 1t+1 Then dxdt…

Q: * Q9 If y = cos(x + y)dx + (3y² + 2y + cos(x + y)) dy = 0, then M = cos(x + y), N = 3y² + 2y Ttue…

A:

Q: d*y _2d'y dx d²y_gdy +4y = 0. dx dx dx Ans.: y= (C, +C,x)e* +C, cos 2.x + C, sin2x.

A: Given the homogeneous linear differential equation with constant coefficient is…

Q: -7x f(x, y) = e" sin(4x + 5y) af e^(-7x)(4cos(4x+5y))-7sin(4x+5y) af 5e^(-7x)cos(4x+5y) dy ||

A: Partially differentiate with respect to x and y by using product rule.

Q: +10 ay +24 y=0. (a) If y= Asin x+B cos x, show that d²y -+y=0. dx dy (b) If y= Axe", show that x-…

A:

Q: 4) (у-сos' x) dx + cos xdy %3D0 5) 2y(y² - x)dy = dx

A:

Q: b) Differentiate y = e (In3x) + tan (3y) with respect to x. %3D + 2e In 3x Ans: dy %3D 3 1-

A:

Q: 1. Obtain the par hicul ar foluhon 4 DE . 9xy dy a. oy dx = ; uh en x= 2,y=1 b. 4xy dy = 2y (I+ y?)…

A:

Q: 7. Calculate dy/dx at the point indicated: f(0) = (7tan O, cos O), 0=/4

A: Here we will use the concept of parametric equation and Derivative of parametric ewyations

Q: (у — сos*x)dx + cos x dy %3D 0

A: We need to find the solution of y-cos2xdx+cos x dy=0 This differential equation can be written as:…

Q: (e* – sin y) dx + cos y dy = 0; when x = 0,y = 1 - %3D

A:

Q: If we have to check the DE (5-8y+4xy)dx = (x+2)'dy for Exact then My %3D

A:

Q: What is the general solution of (2ry – tan y) dx + (x² – rsecy) dy = 0 ? %3D atany 222y 12 sec2 y =…

A:

Q: Evaluate ff, xy.cos yz dx. dy. dz D = { (x,y, z): 0 <xS1 & 0<ysl & 5:50

A: We have to evaluate ∭Dxy⋅cosyzdxdydz, where D=x,y,z:0≤x≤1 and 0≤y≤1 and 0≤z≤π2 Now,…

Q: Use Green's Theorem to evaluate Se xy dx + (1 – æy³) dy where C is shown below y (1,4) (-1,2) 2 1…

A:

Q: dy Find -5 y%3D(2+cos4t) dy dt

A:

Q: 5. (e* – sin y)dx + cos y dy = 0; when x 0,y = 1/2

A: First we will convert the given differential equation into linear differential equation by…

Q: * sin(Iny)dy is equal to y A -cos(ny) + C B none of these cos(Iny) + C y D cos((ny) + C cos(Iny) + C…

A: A standard integral in some cases can be converted to a standard integral with an appropriate…

Q: (dy/dx -y =sin3x) is * O Homogeneous Non Homogeneous O Non of the above

A: The given differential equation is                                                dydx-y=sin3x…

Ratios

A ratio is a comparison between two numbers of the same kind. It represents how many times one number contains another. It also represents how small or large one number is compared to the other.

Trigonometric Ratios

Trigonometric ratios give values of trigonometric functions. It always deals with triangles that have one angle measuring 90 degrees. These triangles are right-angled. We take the ratio of sides of these triangles.