نقطتان )2( What is the Form of the General * ?Solution for this equation A. y(x) = Aem; + Bem;x dy? dy dx2 ' dx 6y = 0 B. y(x) = (A + Bx)emx C. y(x) = e"(c cos Bx + D sin Bx) %3D

Q: f(csc x cot x + 3x2)dx csc x – x3 + c csc x + x3 + c - csc x + x3 +c .3 x° + c O cotx + x3+c

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Q: Cos x sin (sinx) dx

A:

Q: Determine 1 dx , 4x2 +1 (i) (ii) x cos x dx .

A: Determine.  (i).  ∫14x2+1dx             ⇒∫14x2+1dx=14∫1x2+14dx  ⇒∫14x2+1dx=14∫1x2+122dx…

Q: (sin°(3x) + sin²(3x)) cos(3x) dx

A: We have to find the indefinite integral.

Q: QI) Show that: (a) (1+x)° =1+6x (b) (cosx) = –sinx dx

A: 1.  a  1+x6≅1+6xb  ddxcos x=-sin x

Q: ~3 1 (c) dx (x 1) 3. -

A: Given query is to find the integral.

Q: 6. (a) cos 2x dx; u = 2x

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Q: 3dy √1-4y² xdx cos² (x²) 2 4. Solve - 5. Solve - 6. sinx dx secx

A: I am attaching image so that you understand each and every step.

Q: S sin (2x – 1)cos (2x-1)dx (2х - 1)dx

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Q: xsin ax 2 2 (x²-x²) 1/2 Show that [²= - dx - TV J₁ (ay) 2

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Q: Rewrite the following equation with the variables separated. tan(y)y' = 4 cos(x) O sin(y) dy = 4 dx…

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Q: dx (x²+4x+13)3/2 ſcos5(x)sinª(x)dx f) S g)

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Q: sin (3x+1)dx 4 cos (3x+1) C

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Q: y-e" sec! x-3x° 2 csC X Sin x-2X

A: on doing the differentiation of this we get the

Q: (- + 2 cos 2x ) dx + (- - 2 sin 2y ) dy = x2

A: You have asked multiple questions in a single request. As per our honor code, we will only solve the…

Q: d (x2+2x)(sin(x)+5) 7. Find: dx Зx+2

A: To find:

Q: 음 (sin-" (2))\_-+ = (교2)) | dx 2(:) A 1+ 2() B (C 2 (4) cos-1 (16) D -2 (금) cot () csc(6) CSC

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Q: Find dy clx In (sin(8x3)) a) y=(√√x2-1) In (sin( b) y = 1+ sin ² (3x)+sin 4 (3x) + sin 6 (3x)+.... +…

A: Since, you have posted multiple questions.As per guidelines we are supposed to answer only first…

Q: x° + x2 + 1 (c) dx. x3 – x2 +2x - 2 arctan x (d) x2

A:

Q: a.) 4xy" +3x³y'-7x=sin(2x)e²x b.) 5xy+3 dy dx) N = 2e+¹

A: a) The given differential equation is 4xy''+3x3y'-7x=sin2xe2x. Here, all the coefficients anx,…

Q: instead of cube there is a square in that equation 3(2x-1)2 please solve

A: Given,           ∫2x-1cos32x-12+632x-12+6dx

Q: sin(3x - 2) csc(4x + 3)' dM solve for dr

A: Here we can find the derivative as below with respect to x

Q: General Solutions (D2+2D+2)y=5cosx+10 sin2x

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Q: b) S. cos x cos 7x dx

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Q: j dx (2x-3) 15-12x+cx 2

A: As per the guidelines, we can be answered only for first question. Please repost the rest question…

Q: d²y + y = 4 cos x dx² Please solve this equation by hypothesis (V)

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Q: 6メ-8) - $(4)= =1 Cos x (8-x9- 15) %3D

A: Since in part 1st given equation has no rational roots so I will do 2nd question

Q: t 3X +5) C

A: on doing integration we get

Q: S(cscr cot a +4x)dx sec a +x"+c 4. CSc a +x +c sec a+ x"+c O - sin a + a+c CSC a+x"+c

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Q: y = cos³V2x – 1

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Q: (1 point) Check by differentiation that y = 3 cos 2t + 3 sin 2t is a solution to y" + 4y = 0 by…

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Q: b) dx xV5x2 – 4 c) dx 2 + (x - 1)2 d) . /2 2 cosx dx 1+ (sin x)²

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Q: 1. x2 cos 2x dx

A: The given integral is: ∫x2cos 2x dx

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.