dy + 2y = 5t dt %3D For the initial condition y(1) = a, give the domain over which the solution is valid. %3D Describe how the behaviort → 0† depends on a.

Q: Suppose that x and y are related by the equation Proportionality 1 dt. Vi + 4t² |Show that d²yldx²…

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Q: Estimate the area under the line y= 2x+1 using six rectangles and right endponits over the interval…

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Q: Let h(x) -222+z+4 %3D ,what is h' (-5)? 2+4z-1

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Q: Differentiate the function. y = (3x* - x+ 1) (-x³ +9) %3D y' =] %3D

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Q: #2. Researchers have descried the maximum growth rate of a phytoplankton as a function of the cell…

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Q: The temperature at a point (x, y) on a rectangular metal plate is given by T(x, y) = 100 - 2x2 - y2.…

A: Given: T(x,y) = 100-2x2 -y2We have to find the path a heat-seeking particle will take, starting at…

Q: du Solve dt 6u+3t e if u(0) = 2. U =

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Q: State the order of the given ODE. Determine whether the equation is linear or linear. Also explain…

A: Order of differential equation: The order of differential equation is the order of highest…

Q: (8) Find the linear approximation of the function f(x) = Va at a = 25 and use it to approximate the…

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Q: 2 dy 67 +13

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Q: Calculate the first, second, and third derivatives of y(t) = 2016/5 – 6127. (Use symbolic notation…

A: We will use simple differentiation rules to solve this question.

Q: Use a software program or a graphing utility with matrix capabilities to write v as a linear…

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Q: Find y': Vä+1 VI+1 .2 %3D

A: Answer and explanation is given below

Q: Pick the equation that matches the graph below |– x^ Vx 1 O = Vx + 1

A: Given query is to find the equation of the graph.

Q: 8 – t3 17. dt (t – 3) (t + 1)²

A: 17. The given integral is ∫8-t3t-3t+12dt.

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.