The following DE sin(x) +y cos(x) = 1 can be written as: dx Cos(x) sin(x) None of These 1-cos(x). sin(x). dy +y = dy cos(x) : sin(x) O 1-y xp- cos(x) dy O 1-y xp- sin(x) %3!

Q: y"-uy'+5y= e Sin() %3D

A: We have to solve given problem:

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…

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Q: -) Find the general solution of the DE y(4) + 2y" + y = 3 sin t - 5 cos t Use the method of…

A: We can solve this ordinary differential equation by undetermined coefficient

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: Consider the following IVP: y" +y' = -cos x; y(0) = a, y'(0) = b Find the general solution. A y(x) =…

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Q: B\ Suppose that = 4 cos? t , x = v3 sin(2t) and 0 < t < n. S d²y *= - tan(2t) and = -sec (2t). 1 dt2…

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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…

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Q: What is the particular eq. of the given: y"+9y=e^x (cos 3x)+ x² + x³ex

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Q: Let e4 – sin(x + y²) – VTY. Match the following. A. 4e - cos(x + y*) - | - 2 ay B.-2 cos(x + y²) +…

A: Given,f(x,y)=e4x-sin(x+y2)-xyDifferntiating both the sides w.r.t. x…

Q: (cos 2y – 3x²y²)dx + (cos 2y – 2x sin 2y – 2x³y)dy = 0 |

A: We will find out the required solution.

Q: To evaluate 3cos x=1 dr. the integrand can be transformed to 1-sin2x A.) S(3cos³x + csc?x)dx B.) 3…

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Q: The integral / 2/ (*) cos(2*) dx takes the form k cosu du when u=2* and f (x) =x – 5. what is the…

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Q: 4. The value of fx sin(x²+3) dx Acos (x²+) + C C. cos (x²+)+C B. -cos (x²+)+C D. -cos (x²+) + C

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Q: Find dy/dt. 11) y = (ecost/9)4 A) cos e4 cos(t/9) B) sin e3 cos(t/9) e4 cos(t/9) D) - (esin(/9)3

A: Use the chain rule of derivative and simplify.

Q: (a) If y = xV², then dy dx (b) If y = (2 + sin 3x)", then d (2 + sin 3x)" = T(2 + sin 3x)=-1(cos 3x)…

A: We have to differentiate the given functions: a If y=x2, then dydx=2x2-1 b If y=2+sin 3xπ,then…

Q: Answer the following True or False: d Since dx d -sin (6x² + 3x + 4) = (12x + 3) cos x dx (6x² + 3x…

A: The objective of the question is checking the proper use of chain rule .

Q: 11 Evaluate (( sin(y²)dydx where 2: 0<y<1, 0<x<y. 0 x a) 1-cos(x) b) 1-cos(x)) 1 - cos() 2 d) 1.…

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Q: If y = f(x) is the solution of (-x – 9)dx + (x2 + 10x + 41)dy = 0, f(0) = }In(41) +arctan(5/4), then

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Q: 8)find dy/dt for y=cos^2(3#t-1) # is actually pie or 3.14 etc I just don’t have the symbol on my…

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Q: Give the general solution to xу +5ху%3D х 3 sin(4x). a) Oy = x cos(4x) + Cx-5 b) Oy = -* cos(4x) +…

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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: d/dx[(sin x)/(1 - 2cos x)] = (cos x - 2)/(1 - 2cos x)² %3D Select one: True O False d/dx(xe2X) =…

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Q: The sin(5x + 2x) dx cos5xcos 2x is equal to 2 In(sec 5x) + 5In(sec2x) +C А. 10 In(sec 5x) +…

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Q: 3e'x In cos2x Vxy = 1 y? x+1 7 In (xy)-3sin 2y |- 2y = 0

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Q: | 1. Find dx dy for the following functions : 45) y=x' log,(3– 2x) (ans.:3x² log,( 3 –2x)-73-2x…

A: We have to find the following derivatives

Q: 2 2メ Q1 find dy for y = Cos ( In x + e

A: we have to derivative with respect to x

Q: 1- The integration of ſ cos . dx is: (a) sin를 + C (b) 2 sin +C coS x (c) 2 cos를+C (d) + C 2

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Q: The integral / 2' )cos(2*) dx takes the form k cosu du when u=2* and f (x) =x- 5. What is the value…

A: we use the formula ddx(ax)=ax lna

Q: Find the general solution of the d dy 2c-2v = dx 3 sin(x/2)√ √cos³(x/2)

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Q: he Solve the y)-Sy'(x)+8y(x)-4y(x)-xcos(x) equation y,0)-cos(x)+xsin(x)- 41 19 sin(x)+ cos(x)…

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Q: 32. Il sin(x + y) = x,'then dx A 1- cos(x+y) (cos(x +,pv) IB 1+ :aas(x + y) cos(x + v) C cos(x + y)…

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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: Find the general solution of (cos cos y +ycos x ) dx + (sin sin x – x sin sin y ) dy = 0

A: The given differential equation is incorrect and hence the correct differential equation is as…

Q: Solve for Linear DE of Order n: y′′−3y′+2y=cos(e^−x)

A: Using General Method of Linear D.E.

Q: Find . dy dx e 4x, = sin (x + 8y) %3D O In sin (x + 8y) 4e4x -1 S cos (x + Sv) S cos (x + Sv) 4ex -…

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Q: /16 cos (16л x5) dx dy. Os xs 2 Os ys x*

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Q: 1. Find for the following functions : dx 4i) y-bmcx* +2y}kos x (ans.: 4x.cos x - 2 In( x² + 2 )sin x…

A: To find the dy/dx of  y=[ln(x²+2)²]cosx

Q: Solve the D. E. to the I. V. P. sinx(e¬ + 1)x' – cosx = 1, y(곡) = 0 - O (1 + e') (1 + cos x) = -1 O…

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Q: d/dx[(sin x)/(1 - 2cos x)] = (cos x - 2)/(1 - 2cos x)² Select one: O True O False d/dx(xe2x) = 2xe2x…

A: We know that; The Power law: ddxxn=nxn-1 The chain rule: fgx'=f'gx·g'x The Product rule:…

Q: Q4. Given that: z = y sin(2x) + (1+x²)e* + cos x tan-1(y* + 1) In(y6 + 137)

A: Given that, z=y sin2x+1+x2ex+cosx tan-1y4+1 lny6+137 ∂z/∂x is the partial derivative of z with…

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: 3. f(x,y)= In(x cos y)-cos (In3y)+

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Q: Q1:- Solve the following DEs:- ху?-cos x sin x 1) y' У(1-x?) 2) (-4y + e-3*)dx = 4 dy -Зх dy 3) +…

A: We have to solve the given differential equation Here I am giving answer of 1st question if you want…

Q: 1 In order to evaluate dx, the correct substitution is V-x²–4x+21 None of these -2 + 5 sin(t) x = -2…

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

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Q: Differential Equation Activity

A: To find the general solution of the given differential equation

Q: 8. Which of the following is the solution of * [2x + ycos(xy)]dx + xcos(xy)dy = 0 x? + cos(xy) =c x?…

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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

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Q: Find the general solution of the following first-order ODE xy' = y + 2x' sin² (2)

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