Which of the following graphs represents the solution of the initial value problem y" + 36 y = sin(5.5 t), y(0) = 0 , y'(0) = 0 ? 2 O a) 20 25 30 -1 0.3 0.2 b) 0.1 -0.1 -0.2 -0.3

Q: Find the solution of y" + 9y' = 162 sin(9t) + 1296 cos(9t) %3D with y(0) = 5 and y' (0) = 9. %3D y =

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Q: 3. Solve for y in the equation y = e* sin x + e* cos x - y +c

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Q: If y=sech (kx") and (

A: Given,       y=sech-1(kxN)   and (1-289x10)(y')2=Ax2

Q: Solve the given IVP: (a) y""+y" - 2y' = 4e-²x/cosx; y(0) = 0.4, y'(0) = −0.4, y″(0) = -0.4

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Q: y'(0) = 0.

A: Given; Y''+9Y=10 e^-t , y(0)=0 , y'(0)=0

Q: (6) [²/2 sin² (2) cos2 (x).dx = A) 플 B) 플 C) 미플

A: We need to make it proper to solve this integration.

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Q: Find f. a) f '''(x) = cos(x),    f(0) = 7,    f '(0) = 8,    f ''(0) = 8   b) A particle is moving…

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Q: 8) A particle that moves along a linear path has a known velocity of v(t) = 4.3 sin (2.1t), where…

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Q: The equation y" + y' +cos (t) y = e" (9 – t) can be solved by O a) Undetermined coefficients O b)…

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Q: 3-(cos x)y' =yCv-1) sin x.

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Q: Write down the form of a particular solution to the equation y" + 2y + 2y = 5e¯* sin(t) + 5t³…

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Q: (D² - 9)y = 0. (A) y = e*(c,cos2r +c sin2x) B y = c,cosh 3x + c,sinh 3x y = c,cosh – 3x + c,sinh 3x…

A: Solution

Q: 2) Find the minimum value of 6 cos x 8 sin x 3) The phase shift o̟ in a certain electric circuit…

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Q: dy cos?x = -(tan x)y ;y(0) = -1 b) Solve %3D dx

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Q: y" + 9y = e²* sin(x)

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Q: (c) y" + 2y-3y = 9 sin(t)

A: A detailed solution is given below

Q: Solve by variation of parameters method (h) y" + y' = tan x

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Q: Q2/ If the following eq. is exact, then solve it (y cos x + 2xe") + (sin x+ x²e° + 2)y' = 0.

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Q: (2) If y = (sin-1(x))², prove that (1- x2)y" – xy' - 2 = 0.

A: here first we will derivative with respect to x then squaring both side and put value of the y then…

Q: 2) y"+y' - 1 = 3 cos(x)

A: 2.

Q: Find the solution of y" + 4y = 160 sin(4t) + 224 cos(4t) with y(0) = 3 and y' (0) = 2. y =

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Q: the solution to the given equa y" + y' – 2y = cos(x) – 3 sin(: -

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

Q: (i) By sketching the graphs of y = 4 sin x and y= e" on the same coordinate system, find the number…

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Q: 2. Draw the graph z = - cos(y) for 0 < y < 2n, and then use it to help you sketch solutions of y' =…

A: Firstly we draw the graph of z=-cos(y) for the given interval. Then we find the critical points and…

Q: If y(t) is the general solution for the equation: y' + y = sin(t), y(pi/2) = 0 Then, y(0) = ? a)…

A: Consider the differential equation  y'+y=sint,           yπ2 = 0

Q: 47. Show that y = sin(tan-x+ C) is the general solution of y' = /1 – y²/(1+x²). Then use the…

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Q: Nitin

A: (a) y(t)= ±5.83 cos(3t-30.96o)(b) Time period of the motion = 2.09 s      Frequency of the motion =…

Q: Slve the Following initl Value Problems s- a) V+4Y=20 (y=2), b)y'= 2(V-1) tanhx (YCO) =4), c)Y'+3Y=…

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Q: 10. Solve for t on the interval [0, 2π) (a) 2 cos² t-cost-1=0 (b) 2 sin²t-3 sint + 1 = 0 taol al (c)…

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Q: to the I. sinx(e+ 1)x' - cosx = 1, y(=) = 0 %3D %3D (1 + e) (1 + cos x) = 0 (1 + e) (1 + sin x) = 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.