Solve the initial-value problem t Int- dy + y = te', y(2) = -4. dt d. In (2) – 4 – e² In (2)(ln t) y(t) :

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A: From the given problem:   dydt=-3 feet/sec & y=12'   From the given figure:…

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Q: dy (x+1). + y = ln x dx y(1) = 10

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Q: = sin(5x) for y(0) = 2

A: the solution is, y = (11 - cos5x)/5  The detailed solution is as follows below:

Q: 3. (D² — 2D + 1) у %3 е* In a

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Q: Find dy/dx if y = (*+*) А. 1 В. 2х + 2 D. 1/x C. 2x + 4 csc(2b) sec(2b) Find da/db if a A. 2sec (2b)…

A: Hello. Since you have posted multiple questions and not specified which question needs to be solved,…

Q: 5. A termite population begins with 150 termites and increases at a rate of m'(t) termites per week.…

A: Termite population starts with 150 termites and increases with the rate of m'(t) termites per week

Q: d -e'(t² + 5) at t = 0. dt Find

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Q: xy + e^y = ln(x + y) defines y as a function of x implicitly for the most part. Express dy/dx in…

A: Given an equation, Where y is a function of x.

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Q: A(t) = 3000e027z initial investment of 3000 dollars which pays 2.7% compounded continuously. a) Find…

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Q: solve using ODE from t=0 to 2 when y(0)=1 dy/dt= yt^3 - 1.5y

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Q: Find h'(t) if h(t) = %3D t1/2 1617 h'(t)=

A: Given:

Q: dx dt = 10x − x², x (0) = 1 -

A: 2. Given that the differential equation is                                      To find the solution…

Q: Solve IVP: y'''+4y'=x, y''(0)=1; y'(0)=0.

A: Given : y'''+4y'=x

Q: x' = 10 t² x², x(0) = 3 Solve the above IVP and then find x(0.5). Put x(0.5) accurately calculated…

A: Given differential equation is, x'=10t2x2, x0=3.

Q: Solve y'"+ 5y' + 4y = 0, y(0) = - 8, y'(0) = 17 y(t) = %3D

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Q: A population of ladybugs begins with 50 ladybugs and increases at a rate of l'(t) ladybugs per week.…

A: A population of ladybugs begins with 50 ladybugs and increases at a rate of l'(t) ladybugs per week…

Q: Solve y" – 6y' + 8y = 3e, where y(0) = 1 and y'(0) = 3. %3D

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Q: find dy y = ln (1 + x2)

A: The given function is y=ln1+x2. Obtain the differential as follows.

Q: rez If F(x) = -7 sin t dt, then F'(x) =| %3D In x

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Q: find dy/dx in terms of x and y if x ln y +y^6 =8 ln x.

A: x ln y + y6 =8 ln x