Solve the given initial-value problem. 4 -1 -4 X' = 5 х, X(0) [-2e* (2 cos( 21) + 3 sin(2:)), 2eª(4 cos(2t) – 7 sin(2))] %3D

Q: SOLVE STEP BY STEP IN DIGITAL FORMAT 2) [sen² (x) cosª (x) dx

A: The given integral is         I =  ∫ sen2(x)cos4(x)dx           =  ∫ {1 - cos2(x)}cos4(x)dx…

Q: A = (a) Find cos(At) and sin(At) -2 3 (b) Find the general solution of y" + a²y = 0 where a ‡ 0

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Q: Find the steady-state motion of the mass-spring system modeled by the ODE when t = 10 to three…

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Q: sin(a)= 4/5 and cos (B)= -7/25.  Find sin(2a) and cos (a-B)  ,with pi/2<a<pi and pi<B<3pi/2

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Q: Solve the ODE: (3e3 sin y-42y sin(7x)) dx + (e³ cos y + 12y cos(7x)) dy = 0 Entry format: Write your…

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Q: 2 cos a + 3 sin a sin 2α if =-2. 3 cos a - 2 sin a α

A: Sin 2a = 2516​Explanation:If you have any questions please let me know in comment box thankyou.

Q: A. Eliminate the arbitrary constants of y = C₁ sin 2x + C₂ cos 2x + 3x². B. Prove that (y-2)(x - 1)…

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Q: Solve 4x cos(3x) dx using Integration by Parts. 4x 3 + sin 3x + 4 cos 3x + c

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Q: (3) Solve the equations for x and correct the answer to four decimal places. (a) 52-1 = 32+1 (b) 4…

A: Given Equations are as follows As we know that

Q: r Eliminate the arbitrary costants 3X 1. y = Ae cos 3x +Ce sin 3x

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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: 2 १ sin (3x) cos² (5x) d>

A: The integral we are trying to solve is ∫2 sin(3x) cos²(5x) dx. This is a complex integral involving…

Q: 4. Given 0 < 0 < 2n, solve 2 csc x = 3 csc 0 – csc 0 sin 0. 2

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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.