Find if y sin x = x³+ cos y %3D dx 312- -COS I sin z-sin y O 3x +y cos I sin r+sin y O 3z+y cos r sin r+cosY 3-y cos I sin r+sin y

Q: find dy/dx.1. y = -10x + 3 cos x            2. y = 3/x + 5 sin x3. y = x2 cos x…

A: Given the functions :- 1.  y = -10x + 3 cos x Differentiating with respect to x dydx =…

Q: (2y cosx + sin“ x)dx = sin x dy ,when x =",y = 1 5y= 1 %3D X 2

A: 2ycosx+sin4xdx=sinxdy,   x=π2,   y=1:A first order linear ODE has the form of y'x+pxy=qxLet y be the…

Q: 26. da (x² cos y+ sin 2y) =(ry) x(- sin y y') + (cos y)(2z) + cos 2y - 2y = x-y' +y·1 = %3D %3D dx…

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Q: find dy/dx. y = 6*(sin x + cos x)(sin x - cos x)

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Q: g) y ext= cosh x + √cosh²x -1 +7 ex е X h) (3 x y² + 4y) dx + (3 x²y² + 2x) dy = 0 I) sin x dy dy -…

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Q: d³y + 4x². d²y +sin sin 2x dx2 dy 1. dx3 dx =sin sin y 2. y*dx + (2xy +lIn In y )dy = 0 d²x 3. (4y?…

A: Solution

Q: Find dy/dx for: y cosy = xy Y O -y sin y+cos y-x Y cos y-x Y -y sin y-x 1 cos y-x O O O

A: Given :y cosy= xy Use product rule of differentiation which states that…

Q: (e* sin y – 2y sin x)dx + (e* cosy + 2 cos x)dy = 0

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Q: If sin (x – y) = x³ then dy 1s dx а) dx dy _ ycos(x – y) – 3x² хcos(х — у) dy_ cos(x – y) – 3x? b)…

A: Solution is given by using sum and difference identities of trigonometry as follows :

Q: CORRECT to find y'(x). d d v'(x) = (In 2z) x (sin u) y'(x) de dx ..... .... .... d y'(x) = sin- dr d…

A: We have to choose the correct answer from the given options according to the given information

Q: Solve for dy given xsin y - ycos x = 2 | dx sin y-ysin x А. cOS X-XCOs y sin y+ysin x В. coS X-XCOs…

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Q: Solve ODE for general solution: (2ysin(x)cos(x)-y+2y^(2)e^(xy^2))dx=(x-sin^2(x)-4xye^(xy^2)dy

A: Hence the given ode is exact. Obtain the general solution as follows,

Q: If xy+sin y = x², then . dy х — 2у - || dx y + cos x 1. dy 2х — у - dx y + cos x 2. O dy 2х — у ||…

A: Proceed as shown below...

Q: dy + (cos x)y = sin(x²) dx 11. sin x dy – 4y = x*e* 12. x dx

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Q: 2 xy dy – (r' + 2y³) dx = 0 xsin 2 dy y sin- -x | dx

A: Homogenous differential equation: Let us consider differential equation of the form…

Q: e^(x)sin(y)+2y)dx+(2x−e^(x)cos(y))dy=0 Find F(x,y)

A: We have to find the general solution from the given differential equation

Q: dy (=)y = x* sin x. dx

A: Linear differential equation

Q: (ysin x+xy cos x)dx+(xsin x+1)dy = 0 Ans. xy sin x+ y = c

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Q: 9. cos(xy) (x dy + y dx) = 0; y(1) = = 10. [y sec2 (xy) + 1) dx + x sec (xy) dy = 0; y (;) =" %3D 3.

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Q: Find dy/dx 1. sin^−1(xy) = cos^−1(x − y) 2. sec^−1(2y cos x) = x^y

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Q: (b) If f (x, y) = y sin2x + x°cosy °cosy 3 then verify dxðy dyðx

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Q: d = cos(zx); y(0)=1 dx %3D a. y=sin(x) b. y=cos(zx) sin (x) C. y= 1 d. y=-sin(x)+1

A: Given, an initial value problem we need to calculate the solution:

Q: Reducible to Exact (y3+2exy)dx+(ex+3y2)dy=0

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Q: cosxdx 17. secx+ tan x 18. [2sin(3x)cos(5x)dx 19. [(sin y + 2 cos y)'dy 20. ſcot'(2x)dx 21. [sin“…

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Q: Н.W. 2) Inx = dy = 1 dx dy 1) = ex-y 3) /2ху dx dy y

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

Q: dy Solve for dx sin y+ysin x given xsin y- y cos x = 5 А. cOS x+x cos y sin y-ysin x B. COS x+x Cos…

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Q: dy x(2 In x+1) 1. dx siny+y cos y

A: Since you have asked multiple question, as per our guidelines we are supposed to answer only one…

Q: dy cos(x)–+ y sin(x) = sin²(x) cos(x) y³ %3D dx

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Q: (1 + Iny-) (;++i" y) dy = 0; 7. dx + y(2) = 1 Ans: In y+x+xIny-=0

A: The given differential equation is  1+lny-xy dx + xy+x22y2+3yln2y dy =0   ;  y(2) =1 Compare with…

Q: Н.W. dy dx 1) 2) Iпx dy 3) 2ху dy = 1 dx = ex-y dx y 4) хеУ dy3 y х2+1 5) х?у — (1 + х)Csc y dy dx…

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Q: find (x² – 2x + 1)e²* dx dx 9. 10. fun tan - y dy y dy 11. 12. sin- x sec² x dx 4x sec2 2x dx 13.…

A: Hello thank you for the question. We’ll answer the first question since the exact one wasn’t…

Q: g) y² ex+y = cosh x + √rosh²x -1 +7 et h) (3 x y² + 4y) dx + (3 x²y² + 2x) dy = 0 I) sin x dy Sin 2x…

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Q: 1. sinx siny dx + cosx cosy dy = 0 %3D 2. [2xy cos(x2) – 2xy + 1]dx + [sin(x²) – x²]dy = 0 3. y?dx +…

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Q: (2xy + x²)dy + (2xy + y²) dx = 0 A2 (3x² + 2xy) dx + (x²) dy = 0 *A3 (3x²y³ + 3 sin x + 4y) dx +…

A: Disclaimer: SInce you have asked to solve only question 3, this question has been solved only.…

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…

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Q: JJJ y dz dy dx 5. [T" xydx dz n/4 2 sin x cycosx A. ex+y n /2 ccos x T-X I sin(x +y)dy dz dx Ir / 6…

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Q: 25. (y cos x + (2y sen x – xr + In y) dy = 0, y(0) = e 3xy – 2x) dx –

A: The given differential equation is: y2 cos x - 3x2y - 2xdx+2y sen x - x3 + ln ydy=0  ;…

Q: 4) sin x sin y dx + cos x cos y dy = 0

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Q: (2y sin(x) cos(x) – y + 2y e) dx = (x – sin (x) – 4xyey)dy.

A: the differential equation Mdx+Ndy=0 is exact when ∂M∂y=∂N∂x where M and N are functions of x and y…

Q: sin 2ycos 2y cosxdx dx 17. 2. secx+tanx 18. [2sin(3x)cos(5x)dx Vydy 1+y\y 19. [(sin y +2cos y)’dy…

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Q: 3. [cos y + 1]dy + [tan x (sin y + y)]dx = [sin y cos x + y cos x]*dx gettyimages Fuse When:x = 0; y…

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Q: e* tan x dy + xe*y* dx= y* tan x dx A xy(1 – sin x)dx + (x + e* )dy = ye* sin x dr B sin x cos y dx…

A: The objective is to find whether the following are Bernoulli's equation. The general Bernoulli's…

Q: (8 cos x cos y + 4 sin x sin 2y + 1) dx – 8(sin x sin y + cos x cos 2 2y) dy = 0

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Q: 1 If y = sin' x then is dx dy dy -3 cos x b) dx a) –3 sin² x cos x dx sin¯ x dy dy _ -3cosx = -3…

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Q: 4.) Find dy/dx. Given: 5x - x'y' = 2y %3D 5.) Find dy/dx. Given: y? + 2xy² – 3x + 1 = 0 | 6.) Find…

A: 4. 5x-x2y3=2y5. y2+2xy2-3x+1=06.1x+1y=1

Q: Find dy/dx. y = x' sec (-). A 1 sin 3x cos + x sin2 5x (e) B) x sec 5x sec C) x sec sec D x sin 5x…

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Q: 2. Integrate: a) Sx cos(x²) dx g) [3 cos(2nx) dx b) S tan³ x sec²x dx h) Se2% sin(e²*) dx c) S cot x…

A: Hello. Since your question has multiple sub-parts, we will solve first three sub-parts for you. If…

Q: 1. (2xy + x²)dy + (2xy + y²) dx = 0 1000 A2 (3x² + 2xy) dx + (x²) dy = 0 2. *ALA 3. (3x²y³ +3 sin x…

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