Which of the following D.E.'s is Bernoulli D.E. Select one: a. y' + y – sin(x) VJ = 0 b. (y')2 + 2xy = a²y³ c. y'y + 2a°y = 3y3 с. d. y' + 2xy = 3x³

Q: 5. Find : 60 y= (b) y = cos (11x³ + 5x). dx

A: SOLUTION-

Q: d²y Find С. dx? 1. y= sin 2x +cos² x sin x 2. у- - y= 1-cosx

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Q: - Find dy /dx for the given function y? cos fy)=2x +2y

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Q: Which of the following equations is NOT an exact equation OA. (2x sin y + y)dx + (x² cos y + x)dy =…

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Q: Which of the following equations is NOT an exact equation?| OA. (2x sin y + y)dx + (x² cos y + x)dy…

A:

Q: i. L x² 8(x – a)dx ii. L,7t? cos t 8(t)dt L,7t? cos(t – 2) 8(t – 2)dt iii. -

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Q: /2 x cos x dy dx : %3D 0 0 а. О b. 2 C. -1 d. 1

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Q: 11. Which function has the shortest period? A. y 6 sin(3x) + 20 B. y = 8 cos(2x) - 4 С. y 7 соs(x) +…

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Q: d'y Find dx? given that 5xy = 25. Oa. O a. dy 2y 2 dx2 Ob. d'y 2y x2 Oc. d'y ,2 dx? O d. dy dx?

A: Topic:- Derivative Correct option = b

Q: If dy = x cos x² and y = -3 when x = 0, when x = π, y = -3.215 2 1.647 6

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Q: Which of the following is a solution to x² + 3x - 3y = 0² dx² dx a.y = 8 b. y = 2x c. y = ex d. y =…

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Q: * cos Ew) sin Gw) dw 5.

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Q: dy If y = sin(6x – 4), then dx O a. 4 cos(6x – 4) O b. -4 cos(6x – 4) 6 cos(6x – 4) O d. -6сos(6x -…

A: y= sin(6x-4)

Q: 4. In each part below, find dy dx a. y=x³ +5* +55

A: Since you have asked multiple questions in a single request we would be answering only the first…

Q: 3 6. Show that [[[ y sinzdxdydz = (1– cos1). 2 COS %3D 00

A: We have to prove given integral

Q: the order of the d.e. () + cos(x)y= x³ Select one: a. NOTA b. 3 С. 2 d. 0 e. 1 OO O C

A:

Q: Given x = sin3t, y = -cos3t, then find at t =. %3D dx а. 1 b. 3 с. О d. 2

A: We need to find dy/dx.

Q: Which of the following equations is NOT an exact equation? O A. (2x sin y + y)dx + (x² cos y + x)dy…

A: The given differential equations are: A. 2xsiny+ydx+x2cosy+xdy=0 B. 1ydx-xy2dy=0 C.…

Q: If 7x5 - 5y7 = 5x² + 7y°, find dy/dx. dy dx II

A: Given problem:- If 7x5 - 5y7 = 5x2 + 7y5 , find dy/dx.

Q: d 1. Evaluate: dx [V5 5+ (x° + 1)³ d cos* x + sin* x dx 4 4 2. Evaluate:

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Q: Solve the Bernoulli's DE: (x°y3 + 1) dx + x4y2 dy = 0.

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Q: 2. Prove the following equation is exact and hence find its general solution. (y?sinx + xy?cosx)dx +…

A: Given: (y2sinx + xy2cosx)dx + (2xysinx)dy = 0 To prove that the above equation is exact. We also…

Q: If y = sin(6x), then dy is equal to which of the following? dx -6cos(6x) O-1-cos(6x) O cos(6x) O…

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Q: Solve the given IVP. Write your answer in terms of Sine and Cosine if applicable. y" – 4y" + 29y' =…

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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.