What is the solution of given initial value problem? =y+ sin t dt2 d'y dx + cos t dt %3D dt2 (0) = 1, z'(0) = 0, y(0) = -1, y'(0) = -1 %3D %3D %3D O a. z(t) = cos t, y(t) = Cos t - sin t O b. z(t) = cos t, y(t) = - cost +sint %3D Oc. (t) = sin t, y(t) cos t + sin t %3D %3D O d. z(t) = cos = cos t, y(t) = - cost- sin t | %3D O e. r(t) = sin t, y(t) = -cost – sin t %3D

Q: y= cosV1- x y' = V1-x² ² y' = 2v1- x² y' = 2va- x2 y' = Vx-x* 1 y' = 2Vx-x2

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Q: Y'=x/y senx/cosy   y(π/2)=0

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Q: (3e* sin(y) + y)dx + (2x + e* cos(y))dy = 0 not exact

A: Que is not clear though. We Shall check exactness for the given differential equation. If you have…

Q: dy ху? dx. dy - 2y³. - x³ + 2xy? = 0 dx

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Q: Let f(x, y, z) = x'e sin(x yz) %3D 12 find dyəzd' x at the point (2, 0,0)

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Q: y′′′ − 2y′′ − y′ + 2y = e^(−t)sin t by variartion of parameter

A: Given equation  y'''-2 y'' - y' +2y = e^(-t) sin t, say (1)  First we'll find the complementary…

Q: 2 (Dx-2Dx0y +Oy)u= 3Xy %3D AMS. 4

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Q: - 5x² + 2y? = 4 5y² + 3 = x² sin(x + y) = 2x

A: According to guidelines we can answer only three subparts, or first question and rest can be…

Q: dy/dt^2 – 4dy/dt – 5y =0, y(1) =0 ; y’(1) =2

A: Given differential equation d2ydt2-4dydt-5y=0  , y(1)=0 and y'(1)=2

Q: 1. ſ f(x)f'(x) dx 2. S Vx³ dx 3. S csc?x dx

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Q: y" +2y' = 3+ 4 sin(2t)

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Q: xy' + y = 0, y(4) = 6 %3D

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Q: This answer is incorrect, could you please attempt it again?

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Q: y" + 4y" +y' – 6y = 2e¬t + 5 cos t y" + 4y' = 16 sin 2t , y(0) = 2, y'(0) = -2, y"(0) = 4

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Q: 3. Differentiate x²+1 () ± ([** 1 dt 4 1+ sin“ t d dx

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Q: dy if 6 + sin 2y = dx 2y + 3x by using implicit differentiation. 2y + 3x Find Hence, find the…

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Q: Compute the differential dy  for  y=(6x+sinx)^3

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Q: 13. Equation from Exercise 1; y(0) = 1, y(-2) = -1, y(0) = 3, y(0) = 2. %3D

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Q: dy = 1+y² dx y' = yx³

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Q: y" +2y+3y= sint + 8(t-3л); y(0) = 0, y'(0) = 0

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Q: 3x'y*dx + (2a°y + 4y*)dy = 0 Oa²y³ + y* = c Oa'y? + y* = c Oa'y? – y* = c Oa²y³ – y* = c 2.3

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Q: y(1-x^2) dy/dx=x(1+y^2) solution of first order Deferential Equation

A: We have to find solution of y(1-x2)dydx=x(1+y2)

Q: 2- y" + 4y' + 20 y = 23 sin t - 15 cos t y(0) = 0 , y'(0) = -1 %3D

A: Differential equation is, y''+4y'+20y=23sint-15cost Given conditions is, y0=-1y'(0)=1

Q: O Find the derivatives: y%=Sec. 2) y=Secltanx) y=Inf tanx> ...

A: Authoring guidelines:…

Q: y sin 2x + cos 2y = ax Find y' a – y cos 2x y% = sin 2x – sin 2y а - 2у сos 2x y sin 2x – 2 sin 2y…

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Q: cos (Vt) COS 15. dt

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

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.