1. Draw a direction field for the given differential equation. Based on the direction field, determine the behavior of y as t oo. If this behavior depends on the initial value of y at t = 0, describe the dependency. (a) y = 2+ y (b) y = 4- y

Q: Find the differential of each function.

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Q: Draw a direction field for the differential equation y' = sint + 1+ y. Based on the direction field,…

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Q: ay 1. Consider the differential equation dt The solution to this differential equation models the…

A: dydt=yt2+1⇒dydt=ftt2+1 So, the value of derivative at t=0 is  dydt=f00+1=2 Equation of tangent line…

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A: For part (1) We have to find out the second order differential equation of y=asinθ,x=acosθ Use…

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Q: Determine which is the pure time differential equation, which is the autonomous differential and…

A: Given equations:  dfdt=e-t2                 ............................(1) y'=3y+y2…

Q: This is a Dynamics question using differential equations

A: Step 1: Step 2:Step 3: Step 4:

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Q: Let f ={ (-6,4),(-5,3),(4,-6),(3,-5),(1,5),(2,6),(-3,5),(-8,2),(6,4)}  g=…

A: It is known that f-gx=f(x)-g(x) and f·gx=f(x)·g(x). The sets are provided as:…

Q: Rewrite the following differential equation using differential operators. 1. y" dºy Зу" + 4у d³y 12e…

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Q: Write the first-order differential equation in standard form. (Use yp for dy/dt.) dy dt = 7y + ty +…

A: The standard form of a first-order differential equation is dydt+g(t)y=h(t)or, y'+g(t)y=h(t)…

Q: Draw a direction field for the differential equation y'= -10+t-y. Based on the direction field,…

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Q: v = ) V In(2x-3y

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Q: Consider the differential equation y' = et. (a) Draw its direction field. ? A. y = C. LLLLL J.J [TTT…

A: Given differential equation is y' = et ------> (1)Now find the following:

Q: y (t) = cie' + czet – 3te + cos t –

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Q: Draw a direction field for the differential equation y' = y(4 – ty) and state whether you think that…

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Q: 7. Find an equation of the line tangent to the curve y = 3x² – 1 and perpendicular to the line x

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Q: Find the differential of the function. P = 99 - 293/2 dp = X

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Q: dy Find the equilibria of the differential equation = 8y (y? - 81). - 8y (y² - 81). dt

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A: Given differential equation  (x+4y3)dy -ydx=0 (x+4y3)dy=ydx(x+4y3)y=dxdyxy+4y2=dxdydxdy-xy=4y2

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.