9 Jlguull 2(s-1) (s-1)²+9 2et sin3t a O 3e -t cos2t b O e-t cos3tc O .C 2et cos3t d O 3.

Q: Solve the following DE: (r+sin-cose) dr+r(sin+cose)de=0 O r²+r(sin+cos) = C Or+2r²(sin-cose) = C O…

A:

Q: dy sin x Ify= et dx

A:

Q: y=Sin x -37 30 Ly= cos x - 37 -2 77 ST 377 2. HN - 15

A: Answer is mentioned below

Q: - 75ec 3x+tan 3x(sec 3x+tan 3x) cos 3x dx (7sec 3x+tan 3x)In 7 + C 7secax+tan ax + C 7 In 3 3 O c B…

A:

Q: sinx S- cos?x+ 6cosx+13 O In cosx+3-Vcos²x+6cosx+13|+C O In cosx+3+/cos²x+6cosx+ 13 O…

A: To find:

Q: Evaluate: Jcos 2xdx cos2x, cos³2x + C 6 A + 2 cos 2x + C 6 cos2x B sin 2x + C 6 sin2x 2 sin2x sin32x…

A:

Q: n all yER Fim a powes cypnesentation for sehjes growes Y?cos (2x) 4 thn by dfferemtiatinn suow unt…

A: We have to show that the sum of given series.

Q: (4) = - V2 -1 cos 4

A: Given,            cos-122=-π4

Q: Let A = ° -2 [23] eAt = e2t T eAt = e³t eAt = e³t e³¹ = cos(3t) [- sin(3t) cos(2t) sin(2t) [ e37 .…

A: A square matrix A is given. The objective is to find the value of eAt. If A=a-bba, then eAt=eatcos…

Q: Evaluate L{t°e! e3(1 – t) 3e-t sin (4t - 2) 2) + t2 $ (3t)} cos

A: Explanation of the answer is as follows

Q: If Z-1/v2+i/v2 then the value of conjugate of Z^5=?* O cos(3n/4) O 2sin(5n/4) O 2cos(5n/4) cos(5n/4)

A:

Q: Ql:- Calculate the expression sec3.42x-5 +In4 cos30)2-4x 2 where x = 2, y = 5.…

A: Topic-Function

Q: A B 25/sin² 5 (sec 0 - cos 0) d )* Which of the following is equal to S; x² +25 dx ?

A: The given integral is x2/sqrt(x2+25).

Q: (D² – 2D - 3)y = 2sin x a. , =cosx -sinx =-cosx -sinx c. = -cosx +sinx COSX 1 b. yp С. Ур 21 COSX d.…

A:

Q: dt cos (2 sin 21) /1– 4r

A:

Q: L(e²'cos3t) = Select one: a. NOT b. 3 (s – 2)? + 9 C. 3 (s + 2)² + 9 O d. S-2 (s – 2)² + 9 е. s+2 (s…

A: Use the formula below to yield the result.

Q: ∫0π/2[√(cos5t) sin5tdt] Hint: intergration by substitution

A: Rewrite the equation Apply substitution u=√(cos5t)

Q: Evaluate e cosh 2t -3t s13 d) 4(s? - 6s-5) 3. s43 a) 4(s-6s + 5) b) 4(s? + 6s - 5) c) 4(s + 6s +5)

A:

Q: Compute / sin? æ dæ. sin 2x + C 4 sin a +C 3 cos 2x + C 4 2 sin 2x + C 4 cos 2x + C 4 2

A:

Q: Q1/ A: Find: 1 L-1 55+4 2S-18 5²49 24-30 √S + 54 2- L (t² cos at)

A:

Q: -31 - cos 2t . Find 4

A:

Q: de 4TV3 Show that (2+cos8) 9

A:

Q: 1+ sin.x cos²x -dx =

A:

Q: The f sec$30 sin 30 d0 is {A} sec*30 + C 12 {C}-cos*30 + C {D}cos 30 + C 12 {B} sec 30 + C 18 18

A:

Q: sin –9xdx

A:

Q: (Dª + 5D² + 4) y = 0 a. y = c1e“ + c2 cos x + c3 sin x + c4e¯ b. y = c1 cos x + c2 sin x + c3 cos 2x…

A: To find: The general solution of differential equation D4+5D2+4y=0. Given: The differential equation…

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.

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.