Sketch a direction field for dy/dx = 2t+y^2 Use the direction field to sketch a solution curve for the initial condition y(0) = −1.

Q: dy b) Find the equation of a curve if gradient of the curve at point (x, y) is given by- = 2x3 + x…

A: We have to solve the problem

Q: 1 |dx I (sec² x csc* x.

A: Integration gives the function whose derivative is given. It is nothing but adding all to make…

Q: Find the solution of the following differential equation. x²+1 1. xe"dy + dx : 0

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Q: Find the equation for the curve f (x) at the point (x, y) meet the following conditions dy / dx = 4x…

A: A curve is a function with equation of the form y=f(x). A differential equation is an equation in…

Q: Find the value of dy/dx at the point (-2, 1) for the function which is defined implicitly by x²y – -…

A: Differentiate wrt x

Q: Find the curve y if dy = x2 +5, dx + 5, curve passes through (0, 25)***

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Q: Solve: x- dx dy - (x + 1)(1 + y*).

A: First separate the variables than integrate and solve the  differential equation .

Q: Find the point on the curve y = Vx +1 that is closest to the point (5,0)

A: We will use second derivative test to find the smallest distance among point (5,0) and curve

Q: a projectile launched at t=0 (t is measured in seconds) follows a path given by x=30t, y=-5t^2+80t,…

A: Given, a projectile launched at t = 0 second that follows a path x=30t, y=-5t^2+80t where x…

Q: d Find {1+ 2x + 3x*} dx Find the equation of the tangent to y = 1++ 2x + 3x4 at the point with…

A: Since there are multiple questions present and you have not specified which question to answer,…

Q: Evaluate dy/dx if y = (sec2x - tan2x)/(2cos2x-1)

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Q: y-Castesinz şinz

A: The detailed solution is as follows below:

Q: Copy the slope fields (mentioned in the Attachment) and sketch in some of the solution curves. y' =…

A: Given: y'=y(y+1)(y-1)

Q: Differentiate the function. y = (2x* - -x+1) (-x* +3) y' = D

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Q: dy/dx=(3-x-y)/(x+y) by using an appropriate substitution.

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