d?y dx3 Solve - 27y=0 O a. y = ce -3x + e7*(c2cos- 3/3 x+C3sin 3/3 -x) 2 Ob. OBy=c,e3x +e"(c,cos 33 x+ c3sin 3V3 x) (c,cosx + C3sin- 3/3 3/3 2 2 3x Oc. y = ce-3x+e2 "(c2cos2x+ c3sin2x) Od. 'y=c,e3* + e?"(czcos -x + C3sin x) 3/3

Q: хах 3. S cos (2-3x2)

A: To evaluate the integral ∫x dxcos2-3x2.

Q: part b,c,d

A:

Q: Solve Initial value problem i. 8cos?ydx + cosec²xdy=0, y() = dy _ x(r+1) 4y3 y(0) =- 1/V2 ii. dx

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

Q: D3-7D² + 16D-12)y=e^7x + Cos5x + Sin5x

A: Given:

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: 2x - 4x – 8 -.dx Find -3)(x* +4)

A:

Q: 3 -x Evaluate dx

A: Given : ddxe3x3-x2

Q: Exercises To Solve [No.5] 2 dx 05² зах (2) x²+2x+5 9x²-6x+5 -11

A: Solution is here

Q: 4加 T (In cos x) Beca Cos X

A:

Q: Evaluate: L-¹{- (A) B Ⓒe²t (cosh7t + (D) (s+ 2)²-49 e-2tcosh7t 4 e-2t(cosh7t – sinh 7t) 4 sinh 7t)…

A: The objective is to evaluate L-1s-2(s+2)2-49 Inverse Laplace transform using table values:…

Q: Solve using +00 S 0 residues x³ sin (3x) dx 2x² + 1)2 2X

A: Let f(z) be a complex valued function,  then ∫Cf(z)dz=2πi×∑R Where C is closed contour and ∑R is…

Q: sinx

A:

Q: (x? + 3x — 45)dх J«+ 3)(х + 12)(4х — 3)

A:

Q: Solve cosx dx + (sinx)y=1 Select one: O ay sinx + ccosx O b. y = 2sinx + 2cosx + c O c. y = sinx –…

A:

Q: -4x+2 Integrate f6 dx with respect to x using the substitution method. (-2x2+2a-2) COMPLETE THIS IN…

A:

Q: (2x2-x+6)dx (х2—х-2))

A:

Q: e-) 1-2x - x2

A:

Q: +2 y = 3e" cos 2x -2

A: Solution

Q: What is fxe- dx ? -x Oxe xee+C Ox²e-2x 2 + C X -xe-* — e * +C x² e-x 2 + C

A: Consider,

Q: (e) S, In|x| dx.

A:

Q: b) Solve: (sinx+y)dx + (x + cos y)dy = 0

A:

Q: The value of (-1+√3 i)^(1/3) is О 2 exp((2TU/7)^i ) 2 exp((2/3)^i) 2 exp((2T/9)^i) 2 exp((2T/5)^i)…

A: We need to choose correct option. As per Bartleby's guidelines we can solve only one question from…

Q: Solve in terms of t, u"""" + u"""' = 0.

A: Given the differential equation is u"""" + u"""' = 0.  Here the auxiliary equation is r8  + r7 = 0.

Q: Rewrite (6x + 9) cos (x + 3x) dx using substitution of variables. o /3 cos udu o / 2 cos udu o / cos…

A: The given integral is: I=∫6x+9cosx2+3x dx

Rate of Change

The relation between two quantities which displays how much greater one quantity is than another is called ratio.

Slope

The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as: