If z = x2 + y² and x t cos 2r and y = r sint, then %3D a2z is at2 (A) 2 cos²(2r) + 2r? cos?(t) – 2ry sin t (B) -8tx cos 2r + 8t2 sin 2r + 2 sin? t (C) 2 cos? (2r) – 2r? cos?(t) + 2ry sin t (С) (D) –8tx cos 2r + 8t2sin2(2r) – 2 sin? t 2t sin 4r + 2y cos t +r sin 2t (E) –4x sin 2r –

Q: (b) sinr + cos² y 4 P(품,등) 3

A:

Q: L' (s²+4)(s²+9) 3 f cos(2a) sin[3(t – æ)]dx O b) cos(2t) sin(3t) c) None of these 1 * Só cos (2a)…

A:

Q: Which of the following equations are exact?

A: A differential equation of the form  called exact if and only if .

Q: (12) The value of "sin(5x) cos(3x) dx A) 1 B) 2π

A: To find the value of the integration ∫02π sin5xcos3xdx

Q: d'y If x = 3t2 + 4t, y = sin 2t. Determine in terms of t. dx2 -2(3t+2)cos 2t-3 sin 2t 2(3t+2)3…

A:

Q: d dr -x² + e³¹ - tan(x) dy²-sin(y) dy cos(y) +2 d dx -√x+e²

A:

Q: ( 4x³- 6x +5 2+3 cos x dx. 9. Find sin?

A:

Q: What is an equation for the cosine graph shown below? -135 -90 -45 -11 -10 +9 8/ -7 -6 -5 3 2 1 45…

A: Given query is to find the cosine equation of the function.

Q: 27. Evaluate: cos 2) - sin 6 4 /3 /2 2 2 1 V2 V3 2 2 1 V2 2 None of the above. + |

A: Hence option (c) is correct.

Q: You are given that h (x) C = dh dx for a number c. You have to find c. = 6 sin (7x) + 5 cos(7x) 3…

A:

Q: Suppose w = 8x² + 2y², X = 3 cos(t) + 9 sin(t), and y = 3 cos(t) — 9 sin(t).

A:

Q: tan(a+β) ; cosα = −(11/61) for α in Quadrant III and sinβ = −(63/65) for β in Quadrant IV

A: To find: tan(α+β)

Q: sin² (t) = cos² (t) + 0.25 sin² (t) - cos² (t) = 0.25 r. a. = where k EZ where k EZ or or t= O where…

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.