Which of the following graphs represents the solution of the initial value problem y" + 36 y = sin(5.5 t), y(0) = 0 , y'(0) = 0 ? 2 O a) 20 25 30 -1 0.3 0.2 b) 0.1 -0.1 -0.2 -0.3

Q: 3. (4x³y5 sin 3x + 3x*y$ cos 3x) dx + 5x*y* sin 3x dy = 0 y(0) = 1

A:

Q: 2. 1= j tan(4x³) ,sec²(4x²)xdx dx 1- I=31-2x) (In( 5. I= 3. 1= ftan? (3x) sec? (3x)dx

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A:

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A: Solved below

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A:

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A:

Q: 2 3. sin³x cos³x dx OSx Show two solutions. 0.

A: Given  The integration is I=∫0π2sin3x cos3x  dx.

Q: (D² - 9)y = 0. (A) y = e*(c,cos2r +c sin2x) B y = c,cosh 3x + c,sinh 3x y = c,cosh – 3x + c,sinh 3x…

A: Solution

Q: If y=tan(arcsec/x), then dy/dx is x – 1 A 2(x-1) sec2(arcsec/x) B sec2(arcsec/x) 2x D none of the…

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Q: y" + 9y = e²* sin(x)

A:

Q: y + sinx cos2(xy) cos (xy) Ex. 13. Solve dx + %3D .cos?(xy) + siny ) dy = 0. CS Scanned with…

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Q: correct graph of y = sin x, -"sxs 2n and y = csc x, - sxs 2n on the same axis:

A: Solution:

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Q: Solve 1- y"- 6y' + 9y 4e Ans. y Ce +c,xex+2x2er

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A: we need to find the equation of the graph

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A:

Q: 13. A sinusoidal function has an amplitude of 0.75 units, a period of 1440°, and a maximum at (0,…

A: Given, Period=1440°=(1440/180) π=8π amplitude A=0.75 vertical shift K= -3 +amplitude=-3.75

Q: (i) By sketching the graphs of y = 4 sin x and y= e" on the same coordinate system, find the number…

A:

Q: 10. Solve for t on the interval [0, 2π) (a) 2 cos² t-cost-1=0 (b) 2 sin²t-3 sint + 1 = 0 taol al (c)…

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Q: 5. Solve the D.E. y" + 4y = e-*.

A: As per our guidelines we are suppose to solve only first question. Kindly repost the other question…

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.