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: (1+iV3)"+(1-i/3)" %3D 2n+1 Sin(- 3 2" Cos( ) 3. 2n+ Cos( 3. 2" Sin 3. (1-V3

A: Kindly go through the solution and let me know in case of any doubt or further clarification in the…

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: m/2 Sni6

A: Follow next step

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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: 0·1 sin(x)dx X

A: Use the nonelementary integral:

Q: x) dx + sin? x + cos? .2

A: Given integral, ∫xx+sin2x+cos2xdx

Q: Solve 4 sin 2x S1₁= 8 4 -1 -¹x³ + x²-x² +2 dx

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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: x* + 3 dx x² + 3x + 1 4. 00

A: Given: ∫-∞+∞x4+3x2+3x+1dx

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A:

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

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Q: 8 csc? 4x cos(cot(4x)) dx sin² (cot(4x))

A: Here, I will be using method of substitution to solve this integral. You can assume:…

Q: 9.) y(4) + 2y" +y = x² sinx

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Q: Find L{cos() + sin(;)}

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Q: 2+ cos (1 + x»'½) .0.5x dx 22 cos (1+x³/2) V1+0.5 sin x 2,0.5x dx|

A: By using Simpson/Trapoizodal rule.

Q: sin(48) cos(48x) dæ : О576 O -2 O 2

A: We have to find the value of definite integral

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Q: Cπ/2 sin² 3x dx

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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: 1. Find (2r – e") dr

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

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.