2) f(t) = 4t3 sin %3D

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

A: Solving integral

Q: Find the general solution of dy dy dx =sin 2x dx

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Q: 2. Obtain the general solution to the equation dy dx x sin x y cos y

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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: 2. 2x?cos y dy + sin y ( x+ siny)dx

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Q: ( 2x – sin y) dx – (x cos y) dy = 0 -

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Q: // sin(7x²) dx dy. Compute O y/3

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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: cos 2x dx (b) 4 cos t dt 0 2

A: Since you have posted multiple questions, we will solve only first question for you. To getremaining…

Q: 4. (2y cos x + sintx) dx sinx dy 5. y' = 1 + 3ytanx %3D

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Q: Find the general solution of 2ydx + (x – sin Jy)dy = 0.

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Q: If y = (4x) sin ( 3z) then %3D dy dx (Be sure to express your answer in terms of x)

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Q: If y= sin f dt, then dy is dx 2x sin x sin x 2 VX sinx 2x sinx

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Q: b. sin 2xdy – 2(y - cosx)dx = 0; when x = 1/4, y = 0

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Q: 5 sin“(3t) dt

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Q: find dy/dt. y = sin (cos (2t - 5))

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Q: | cos 3y dy 4.

A: I=∫ cos6(3y) dy3y=tdy=t3Integration by parts;∫uv dx=u∫v dx -∫ dudx ∫vdx dxI=13 ∫ cos6t…

Q: 2 (b) - 2y dx +(2y tan'(x )-2x +sinh (y))dy = 0

A:

Q: 1. Solve (cosxcos y+2x)dx-(sinxsin y+2y)dy=0

A: (cosx cosy + 2x)dx - (sin x siny + 2y)dy = 0 => cosx cosy dx + 2x dx - sin x siny dy - 2y dy = 0…

Q: 1. S e sin 4x cos 4x dx 2. S dx Je-2x dx e 2x

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

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Q: 8/ (e* sin y +3y)dx -(3x-e* sin y)dy = 0

A: Given thta  The differential equation

Q: find dy/dx if y = (sin-1 x)2

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

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

Q: 7. 2r tan y dx + sec² y dy = 0

A:

Q: -TL 4.) x² sin(xy) dydx

A: Given ∫0π∫01x2sinxydydx

Q: dy Find dt 4 y (1+ sin 7t)

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Q: Solve the equation xcosy dy+(x+2)siny dx=0.

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Q: H. \ || 20 s s sec (cosx) dy dx siny 3y steb e dx dy >+

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

Q: In integrating the function fx cos(3x) dx using integration by parts, what would be your v?

A: Solution

Q: The Integrating factor of the equation (x²y³ + xy) dy dx 1 is

A: We have to find the integration factor of the equation x2y3+xydydx=1. We know that integrating…

Q: find dy/dt. y = sin2 (πt - 2)

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Q: S. use "Exact Equation" method (cosxcosy + 2x)dx-(sinxsiny + 2y)dy = 0

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Q: (c) Solve the IVP x(1- siny)dy = (cosx – cosy – y)dx.

A: Given,          x(1-siny)dy=(cosx-cosy-y)dxand            yπ2=0

Q: 2. sin y(x + sin y)dx + 2x² cos ydy = 0

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Q: Integrate by parts (3t+t2)sin(2t)dt

A: Formula for integration by parts where f and g are 2 different parts             f' and g' are…

Q: 4. § xe¯ dx 6. |t sin 2t dt Jx² cos mx dx 8.

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Q: The integrating factor of the equation (2 + y + x) dx + xydy = 0 is

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Q: 5. Find dt ,y = cos(sin(t – 4))

A: Given function is: y=cossint-4 Derivation of the above function with respect to t. dydt=ddtcossint-4

Q: 3. Find dy dx y= 3 Sin.

A: Find derivative

Q: find dy/dx 19) y=Sin" (5x' ) 24) y= Sin 2x.Cos2x 42) y = sinh (tan x)

A: These problems can be solved by the application of Chain rule.

Q: (2xsinx +3 cos y)dx-3x sin ydy 03 ....

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Q: Can you help me step by step?

A: Given information:

Q: (a) f* (1 – cos 3t) sin 3t dt,

A: Since you have asked multiple questions in single request.so we will answering only first question.

Q: Find the general solution of the equation dy + (tan t) y = cost dt

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Q: dy Find dt y = tan ( sin (4t - 3))

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Q: 25. (2y cosx + sint x)dx sin x dy , when x =y = 1 %3D %3D

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

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Q: (2e" sin(y) – 4y)dr + (–7x - e cos(3)dy = 0 not exact

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Q: Find the integrating factor for the equation dy + sin(3x)y 223 dr

A: find the integrating factor