(ix) f(t) = e-2t sin3t (xi) f(t) = 2e'(cos3t – 3sin3t)

Q: The solution of the differential equation tan xdx + tan ydy = 0 is

A: Using variable separable method.

Q: 7- cos y dx + (x siny - cos²y)dy = 0

A: Note: as per guidelines we support one question in one request . kindly repost next question in next…

Q: 1- Differentiate. a- Y= 2 e2+1 b- Y= -2 sin?x c- Y= 3sin2x - cos 4x d- tanv(1-x)

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Q: 3. cos y sin 2x dx + (cos² y – cos² x)dy = 0

A:

Q: 2 tan(4x-1)-3 cos² (4x-1) If we let u = 4x – 1 for the dx, what will be the resulting integrand?…

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Q: (a) [(0.6e15 + 4t 3t² +03-10-01 at 4t4-3t3 + 0.3 _10t 1.5 -0.1 2t3 (b) Evaluate…

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

A:

Q: 18) e2x = sin(x + 3y)

A:

Q: 8dx 5x+2 xdx 3+Vx S sin1º (x) cos (x)dx .7

A:

Q: Can you help me step by step?

A: The given function is,

Q: [y²e + √elnx dy-(xy) sin² ( * O) + (---) (-) sin² tan² ,dx ey+Inx dy y(In2x-lny) -ex. dx = 0

A: We can solve this using substitution method of ordinary differential equation

Q: 6. Solve y sin (x) cos (x) with initial condition y'(7) = 1 and y(7) = 0.

A: y = 1/4 [ x - 1/2 sin2x] +x -π/4

Q: of (e² 2-X Sin (2y)

A: Given, f= e2-xsin-1(2y) To find, df/dy.

Q: y f(x)sin2x + g(x)cos %3D x) =tan3x x)% sin3x %3D - r) =cos3r

A: Differential equation: y''+9y=tan (3x)The auxiliary equation is,m2+9=0m=±3iComplementary function…

Q: Solve exact equation 2x -)dx + (2x cos(2xy) + 8e²")dy = 0 x² + 1 (2y cos(2ry) + with initial…

A: We will solve the problem.

Q: dy +(cos x)y = sin²(x) using first order linear differential equation. dx Solve (sin x) %3D

A:

Q: Evalualte! dx cosX x+ メ+ 1

A: Given:

Q: 5.32. z = sin(x² + y?)

A: To find the differentials of third order.

Q: S" sin" (0.5x)cos (0.5x)dx

A:

Q: 1) If y = (x-a)√2ax-x² + + a is constant. x- -1(*-ª) ,then y' = 2√2ax - x² a² sin-¹ a²

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Q: dr 1- y = Inlog 2- y = (cos x)*Snx 3- у e (sinx

A:

Q: 1. Find the y" of y = (4x - 3x + 1) (5x + 7) 2. Find y" given y = cosx + sin 3x 3. Find all the…

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

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Q: 3e"dx 3x 1. 3x – 16 2. x 10 – 3x°dx 3. / In (cos®) an@ de 3.

A:

Q: e2x dx 1. Зе2x+1 2. sinx dx 1 3. cos 2x

A: As per bartleby guidelines we are supported to answer only first three subparts,  kindly repost…

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

A: We will find out the required solution.

Q: 2. 1- x2dx cos(x + 1) dx 3.

A:

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

A:

Q: 2. sin3x dx + 2y cos 3x dy = 0

A: Given equation - sin(3x)dx+2ycos33xdy = 02ycos33xdy =-sin3xdxydy =-sin3x2cos33xdx             Taking…

Q: Q1: a) Solve differential equation (2y cos y – x sec y - x tan y)dy = (1 + sin y) dx

A: As per our guidelines, we are supposed to solve only first subpart. Kindly repost other subparts as…

Q: 6 Evaluate (a) [ a + (4x-2° dx + (4x-2)* dx (2x-3)2 2x sin (x²+!) cos (x+1) dx

A: AS mentioned by you that "none of these is graded please answer 5. These are practice questions"…

Q: -2/√√/3 dx x√√x²-1 • [²/²2 (x + 12/²3). dx sin² π/6 28. • √2 30.

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Q: f(x)=X +Sin -1 く(-2)- 4-て+Sini-て)-\no9651 3(x)=てメ+ cosx ずし-て) ニ -4ACOS(-て)-3 (x)-2-らinx f(-2):…

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Q: Q2 Form a differential equation from the function y = (4– 2 cos x) x)cosx.

A: Given below the detailed solution

Q: Cos 5x dx 3 +Sin 5x 1. 2. dx J16-9 (n x)²

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Q: 1. S(tan -1) dp 2. sin2 B cos ß dB 3. S: xdx -7-8x-x

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Q: (1) x(x + 2)² dx x-x² (3) 4+x² dx e²x (2) 2) 14+720x dx J ex (4) | sin³2 sin³2 x sin 2x dx

A: According to bartleby guidelines when student post more than one question then expert must have to…

Q: (一 - dx t - 3 X*cos(3)-4-2 ) -)dy=0 = 0

A:

Q: 3. x = 2 cos(3t) – 4 sin(3t) and y = 3 tan(6t) at t = 2

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Q: 4 sin' 2x cos 4x dx 4.

A:

Q: z sin(2- 32)+cos(2 - 3a)+c | 4x cos(2 – 3x) dx 4x cos(3 3r) dx Option 1 Option 2 |4 cos(3- 3z) dr…

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Q: 4. [(3sin 2f – 3 cos 5t )dt 5. sin x dx cos x

A: 4) Given:            ∫3sin2t-3cos5tdt       =∫3sin2t dt-∫3cos5t dt taking constant out…

Q: 1. / cos" (2t) sin² (2t) dt

A: 1.

Q: 5 dx 3 dx, x> Find V25x-9 0 sin 13x+c -13x+C InV1+9x +3x +c 5x 25x2-9 in 3 + C 3 In 5x 25x2-9 + C 3.…

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Q: (1) ſ [ (x³ + 2 + 7 ) dx (3) cos³x dx (2) √ x³ (2) x3 e3x+1 dx (4) sin x sin 2x dx

A:

Q: 2-€2x y") edxtcuxe yd-siny)lye.co

A: A differential equation of type   P(x,y)dx+Q(x,y)dy=0   is called an exact differential…

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: 1. S(esin *cos x – acos 2x sin 2x)dx 2. S(etan x sec x- esecx tanx)sec x dx 3. S dx xvax - 16 3x-2…

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Q: 16. √(16-9x²) dx 17. dx/ (9x² + 4) 18. sin³ x cos x dx 19. f (secs x) dx/csc x 20. Stan² x dx

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Q: 2. sin3x dx + 2y cos³3x dy = 0

A: Given- sin3xdx+2ycos33xdy=0 To Solve- The above differential equation.

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.