Integrating Factor by Formula a.) (2y²+ 2y+ 4x²)dx + (2xy + x)dy = 0 b) y²cosxdx + (4 + 5y sin sinx)dy = 0

Q: 2. /1+ cos² x dx dy = ? Isin¬' y -2/2 1 (a) 3 3 2/2 (b) 3 3 -2/2 (c) 1 3 3 2/2 (d) 1 3 3 V2 1 (e) +…

A: Given is multiple definite integral.

Q: Solve y y (x, 0) = 3 sin 2n x, y (0, t) = 0 =y (1, t); 0 0. %3D

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Q: 2 sin (t) cos (t)d J

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Q: Homogeneous Find C, if y f(cos 2n) = tan 45° 3(3x + y?)dx-2xydy 0

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Q: 1.5 3-y QI) Evaluate the integral dx dy using polar coordinate

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Q: 2e**+11e3x+16e²x V. e2x+5ex+6 sin2x vi. S -dx cosx+cos*x-2cos²x

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Q: 1. x siny + x²y = c 2. xy² – 1 = cy 3. x = A sin(wt + B), w a parameter, not to be eliminated -

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Q: y'of y = e-2*sin 3x

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Q: 31. (a) 32. (a) 33. (a) 12x-1| dx √2 + x) dx e* - 1| dx L'i lex -3π/4 (b) cos x dx (b) [*/² | } −…

A: Given: ∫-11ex-1dx

Q: i) f si sin 3x cos 3x dx ii) [ cos³x dx

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Q: (2xy-tany)dx+(x^2-xsec^2y)dy=0 solve using exact equations

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Q: (f) ) (3x − 1)√√x² + 2xdx - (8) / sin". (h) [ sinh r cos adr sin x -dx √cos5 x

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Q: (6e + 6x°+ 4 cos a + 2)dx 6e + x° + c 4 cos a + 2x +

A: Since this is a multiple question, according to the Bartleby answering rule, only first question is…

Q: (iii) y= x'e**, y = sin x+eec* (iv) sec x

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Q: (i) y = x® +- vx ++ 2 4 -Vx + + 10 | (ii) y = sin (cos(x2 + x)) %3D

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Q: sin' y 3 Find the particular solution of xsin?y cos y y' +: 1+In x = 4 :y(e) =

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Q: The equation below is said to be - 1 attachment - 3 (d²y\ dy (x² – 1) dx sin x – x + ye2x+1 X dx2 O…

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Q: iii- y +y tan .* sin 2x, y(0) = 1. (Bernoulli Equation) %3D

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Q: (c) The displacement, x, of a particle in simple harmonic motion is given by x = cos(3t) – sin(3t).…

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Q: The equation below is said to be 3 dy (x² – 1) \dx, sin x — х - + ye2x+1 %3D O A. Linear and…

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Q: 2 X 1 t3 COS 4- x² dx 2 -2

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Q: 4) y'-4y = 2x-4x 6) y'+2y = cos(x) 8) y'=(y-1)cot(x)

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Q: The equation below is said to be - 1 attachment - (d²y' 3 (dy sin x – x (x² – 1) ( + ye2x+1 dx2 dx,…

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Q: V.P. [ -8 COS X (a²-x²) -dx, (a> 0).

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Q: [(cos 2y) – 3x?y²] dx + [(cos 2y) – 2x(sin 2y) – 2x³y] dy = 0 %3D

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Q: sec 2x cos? ydy - (1 – sin y) dæ = 0

A: Given query is to find the solution for differential equation.

Q: sin x = x (1 + tan y). Find and provide solution for dx/dy

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Q: B. BERNOULLI'S EQUATION dy 1) nx- 2y = -kxyl-a

A: As per the company's guidelines we are supposed to solve first question for you, kindly repost other…

Q: cos² x sin x dy + (y cos³ x - 1) dx = 0

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Q: 2 (i) xe" dx -2 (ii) -2e" cos x dx (iii) x sin x dx

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Q: esin a x b. COs x dx 0.

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Q: 5. (4xy-y²+10x²+sin x)dx+(2x²-2xy+ cos y )dy=0

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Q: i- y' + 2y 4 cos 2x. yT) = 3 (using Bernoulli Equation) %3D %3D

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Q: x cos x² 2. X C0 dx -siny

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Q: 2. cos æ /1+ cos² x dx dy =? Jsin=' y -2/2 (a) 1 3 3 2/2 (b) 1 3 -2/2 1 (c) + 3 3 2/2 (d) 1 3 V2 (e)…

A: Properties of integartion  To determine ∫f(g(x))g'(x)dx Put t=g(x) the integral will be…

Q: XZ 3) cos(x)-x²y + e + yz = 4, P (0,1,2)

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Q: y = cos x, y= sin 2x, x = 0 and x = 2

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Q: 2. (2xy-tan y) dx + (x²-x sec² y) dy Answer: x²y - x x tan y = C. = 0

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Q: [2xy cos(x²) – 2xy + 1]dx + [sin(x²) – x²]dy = 0

A: The solution attached :

Q: dy 7. S- y vy2 -6y + 5

A: Here we have to integrate the given Integral.

Q: i+ cż + x = cos t, e>0.

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Q: 25) y" + y = 2 cos(t), y(0) = 2, y'(0) = 0.

A: Use second order differential equation

Q: Q-4) Find the general solution of the Cauchy-Euler equation x'y"+ xy'+4y = sin(In x)

A: Solve the Cauchy Euler differential equation

Q: 6. J1-cos I COS T dx

A: Answer is mentioned below

Q: Homogeneous Equations [x csc() – y] dx + xdy = 0 O In = cos() In/cos(;)| = = CX

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Q: y = cos 3x a. 3 sin 3x b. - sin 3x c. sin 3x d. -3 sin 3x с.

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Q: An equation of the tangent line to the curve y = sin(x) at x = 4n/3 is y = + -(х — 4п/3). An…

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Q: y = tan x sin (2x)+cos (2x) 2 y' = A sin (Bx) + Ccos(3x) 3. A = B = C =

A: Hey, since there are multiple questions posted, we will answer first question. If you want any…

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.