The IVP has a unique solution defined on the interval d²r dt² sin(t)- da + cos(t)- + sin(t)x=tan(t) dt x(1) dr dt 1 = 4 =

Q: Suppose h(x) = cos(tť² )dt Calculate h' (x).

A: Given: hx=∫0x3cosπt2dt.

Q: X = cos 2t, y = cos t, 0 <t< n

A: given x=cos2t and y=cost interval 0&lt;t&lt;π  dx/dt =d/dt(cos2t) dx/dt=-2sin2t And dy/dt=d/dt(cost)…

Q: Verify that y(t)=C_(1)sin5t+C_(2)cos5t is a solution of y''(t)+25y(t)=0

A:

Q: ind positive constants b and n, such that 3n + 2 n.

A: Finding the values of b and no

Q: sin t 元 If F(x)= [ dt, then F" 1S 1+cos t

A:

Q: Integrate the function. S dt o. O. V6-R+ sin'1 6t + C 6t o. + C 612 o. 6t 16-12

A: We can find the integral as below.

Q: Find r'(t). 13 r(t) = 3 cos (t)i + 5 sin (t)j + k %3D r'(t) %3D

A: Given:

Q: Let F(x) | sin (4t?) dt. Find the MacLaurin polynomial of degree 7 for F(x). 0.8 Use this polynomial…

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Q: Calculate :| t' sin(t) dt [Hint: At some point in the solution, it might be helpful to write t as t2…

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Q: Find the general solution to the linear ODE. Use each method (integrating factors and educated…

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Q: y = tan o (sin 67E-TT) find dy dt ()

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Q: 4. a) Find the general solutions of the following differential equations. Express the general…

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Q: Show that y sin x is a solution to xy" + (2 secx)y' + xy = 2. =

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Q: Find the general solution of the inhomogeneous second-order linear ODE 2( 24" - 5' 3u)= 2(10 sinx)

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Q: Let f(x) = 1 + x³ + dt. Determine the value of (f-1)'(0).

A:

Q: Js sec¹ (t) tan(t)dt

A: The given integral is .We have to solve this integral.