Consider the non-homogeneous O DE y +2 y +2y = sin 2x using undetermined coefficients method, the form of Ye is CA Yp = x(C, cos 2x + Cz sin 2x} %3D 08 Yp = C cos 2x+ Cz sin 2x Oc e = e( C cos 2x+ C2 sin 2x ) 0o o = x?(C, cos 2x+ C2 sin 2x )

Q: 7. What is the value of (X-2)2 for the scores 2,3,5?

A: To find : ∑X-22 for the scores 2, 3, 5

Q: Prove using the IVT cosx = cos-1x has a solution in (0, 1).

A: cos x = x   rearrange to x - cos x = 0

Q: c) y = (x-2) 3 x² (x-1)(x+5)4 [Hint: use logarithmic differentiation]

A:

Q: sin (2t + 1) - dt cos? (2t + 1) 31.

A: Use trigonometric substitution method for solving the integral.

Q: -2 cos(6t) dt J (10+4 sin(6t))²

A:

Q: Find dy dx 1) y = -1/323 ; tan 43 2 y = sec 5x 3) y = cos cos 2x + tan¹ \/ / 4) y = cot²¹ 2² 2 5) =…

A: Note:-Since you asked multiple questions, according to our policy we can answer only first question…

Q: 1) - 3dx 2) (2-3x)² dx 3) x sin (2x2 - 1) dx (2x-3)2 4) sin3x cos² 3x dx

A: Step 1:Step 2: Step 3: Step 4:

Q: find | cos*x dx 1 1 1 А) — — х —- sin2x + —x + — sin4x + c 4 1 B) =-x +- sin2x + X 4 1 8 1 x + sin4x…

A:

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.