Which of the following differential Equation is Bernoulli's differential equation ? dy + y sin æ = tan æ y" da dy x + y + 2 dr x² + y? dy + 2y sin a = cos æ da dy + y sin æ = e² da The complementary function(C.F.) of the differential equation (D³ – 8)y = sin 5 , is O 5cje2 + e= c2 cos v7x + c3 $in v/7x| O cje2z + e = c2cos /bx + cz sin / - C2 cos /bx +cz sin Võx C2 cos v3z + c3 sin v/3r COS Cje2z + e C2co8 V5x +cz sin v5æ|

Q: x= 4 sin t - 4, y = 4 cos t -3 Eliminate the parameter t

A: we can eliminate 't' . sin2 t + cos2t =1

Q: (c) Prove that sin x 7C sin 2 x2 dx +4x+5

A: The integral function is ∫-∞∞sinxx2+4x+5dx

Q: y = = esin 2x + sin(e²x)

A:

Q: check whether this equation is true for all x:  dy/dx=y(x)   A) Check if y(x) = A sin(kx)…

A:

Q: TT/2 S,"/e cos?x.sint x dx in tegralinin bulunvz sonucunu

A:

Q: Find the differential equation that corresponds to the following solution. Give your answer both in…

A: The given solution is: y=C1 sin(4x)+C2 cos(4x)+C3 x sin(4x)+C4 x cos(4x)

Q: c) i) Find 2 sin cos (1 + sin 8)³ 1) Solve the differential equation sin 2x cos² y (1 + sin x)³ IL…

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Q: Exercise 2. Solve, for z, the equation Inz = 4 – 3i. Exercise 3. Show that (a) sin z = sin 7: (b)…

A:

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: 3x d. Evaluate dx COS cos (3t – 1) dt

A:

Q: Which of the following trigonometric equations has a phase shift of 1/3 to the right? Oy = cos(x +…

A:

Q: Find the solution. dy sin x x-+2y +2y = y (2) = 1 dx (A) y = (4 + sin 2 + cosx?) /x2 B в су %3D (3 —…

A: Given differential equation  xdydx+2y=sin xx,   y2=1 Linear differential equation with initial…

Q: y = sin(Ax + B)

A: We will find the Differential equation as following.

Q: Solve cos x(e2y - y) = e' sin 2x, dy dx

A: We have to solve the given differential equation.

Q: dy 1. Solve the equation x2. +x y= 1. dx

A:

Q: Find the solution. dy X-+ 2y = dx sin x y(2) = 1 A cy = (3 – cos 2x – tanx)/x? B x = (2 + cor2 –…

A:

Q: 1. Find (2r – e") dr

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

Q: a) Verify that the functions y₁ "1 y + 4y = 0. cos(2x) and y₂ = sin(2x) are solutions to this…

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Q: d (cos² 2x)=-2sin 4.x dx 12 Show that %3D

A:

Q: Svæsin(x3/2)dx= A © cos(x/2) + C 을cosx/?) + C D

A:

Q: 5. y + 4y= sin x + 3 cos x Ans: y = C₁+C₂ cos 2x + C3 sin 2x + sin x x-co COS X

A: To solve the given differential equation.y'''+4y'=sin x+3 cos x

Q: The solution of the following Bernoulli's equation xy' + 2y = x¹(cos x) y² is

A: The correct answer is not given in options.The solution with the correct answer is given as

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.