dy (ycosx + 2xe") + (sinx + x²ev – 1) = 0 - dx

Q: (a) | (2x cos y + sin x) dx 6. */2 (b) I| (2xcosy+ sin x) dx dy

A: Solving integral

Q: (3e* sin(y) + y)dx + (2x + e* cos(y))dy = 0 not exact

A: Que is not clear though. We Shall check exactness for the given differential equation. If you have…

Q: dy Find of y=: dx InIn2r

A: We need to find derivative of y.

Q: Find dz/dx and dz/dy for: x² sin (y³) + xe32 – cos(z²) = 3y – 6z + 8

A: Here, the given equation is: x2sin(y3)+xe3z-cos(z2)=3y-6z+8...(1) So, z is a function of x and y

Q: // sin(7x²) dx dy. Compute O y/3

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Q: 7 Find dy (b) x siny-ycosx-y = 1. dx

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Q: y = x * (sin 1x)² – 2x + 2v1-x² * (sin-1x), Find dy dx

A: Given that equation of y and we find dy/dx. We know that d(sin-1x)/dx = 1/√1-x2. And d(xn)/dx =…

Q: find dy/dx if y = sin-1(1/x)

A: Here given as

Q: dy Find for three only: dx 1) y = In(cos x . Inx²)

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Q: 5y + sin y = x²

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Q: dy sin(2x) Find for y || dx /3 – x2 dy dx II

A: Doing the proboem by obtaining the derivative.

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: find dy / dx if y2 - x2 - sin xy = 0.

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Q: integral of sin^6 y cos^6 y dy

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Q: 5. sinx+ cosh2y = 0. dy 6. /2xy -= 0. dy y

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Q: dy x COSY dx - siny=0 6 xcos)

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Q: 2- X %3D +2 3- Coshx dy +(y sinh x+e) dxo 36

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Q: Integral of sin^3 y cos^5 y dy

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Q: Q2 Integrate by parts: ex sin x dx

A: find ∫exsinxdx we know, ∫u.vdx=u∫vdx-∫dudx∫vdx now, apply this on equation I=∫exsinxdx…

Q: 1) ſ y³ sin(2y) dy

A: As per our guidelines we are supposed to answer one question , kindly repost the remaining questions…

Q: dy +cosh 2y=0 dx 3. sin x ans: sinh 2y-2cosx3Dc

A:

Q: find dy/dx where y=sin^3x+cos^6x

A: Given:

Q: Find the value of dy/dx at (1,0) of 2re" – In() = 4y² + 2a sin

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Q: sin(x + y) dx (3x − 2y + 1) dx + (3x - 2y + 3) dy = 0

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Q: x + y sin 2 ) dx x sin 2 dy = 0 -

A: The solution is given in the next step.

Q: find dy of X sin 2y =YCO52X

A: Given: x sin 2y=y cos 2x To Find: To find dydx.

Q: dy 4 sin 2x, y = 2, when x = 1/2 dx

A:

Q: dy Find for dx 3) y = In(vx2 + 1+x) sin¯1x X.

A:

Q: dz Find dy x sin(2y – 5z) =1+y cos(6zx)

A: Given x2sin2y-5z=1+ycos6zx. To find ∂z∂y.

Q: Q) - Find of y = sin de dy ! -11

A: Siny = 1/x.

Q: 10. J(3x3 — 5х + sin3x) dx -

A:

Q: ( cos x - 3xy- 2x) dx + (2y sin x – x+ In y) dy = 0, y(0) = e

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Q: dy Find at x=0: dx y = (In(cos "x*) -1 COS sinh x %3D

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

A: Given - 2ycosx + sin3xdx = sinx dy , when x = π2, y = 1 To find - Solve the following differential…

Q: (continue solution of de) (2ysinxcosx - y + 2y²e*Y" )dx = (x - sin²x - 4xye*y" )dy

A: Using method of exact differential equation.

Q: 3. у?dx— x(2х + Зу)dy %3D -

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Q: 2. f" S"(sinx + cosy) dx dy

A: Note: As per our company guidelines we are supposed to answer the first question only. Kindly ask…

Q: ( cos nx dx= [cos %3D nx cos nx dx 0. %D

A: We have to find the integral of cos2nx dx from 0 to 2pi.

Q: Ans: y-x+ In y+3, dy = 7. ху+3x-у-3 dx ху-2x+4y-8

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Q: Find dy. y=tan-1(ex^10)   dy=(______) dx

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Q: Find the differential dy when x = 3 and dx = 0.2 %3D

A: When you get function of function form to differentiate, we use the chain rule. y = f(g(x)) dy/dx =…

Q: 4. cos x dy + y(sin x – 1)dx = 0; when x = T, y = -2

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Q: Find dy/dx.   e4x=sin(x+3y) dy/dx=

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Q: dy ху* - сosx sin x . У (0) -2 y(1–x²) dx

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Q: dy 1. sin 2ycos2y

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Q: dy for y = dx 9t -dt. 9t + 1 iz's rule to find

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Q: dy sin: 8. x +2y = dx y(2) = 1

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Q: Find dy/dx Find dy/dx y =x² sin°(2x²) x*y? = 1

A: To differentiate y=x2sin2(2x2), with respect to x, use the product rule,…