Consider DE x' (t) = c + x(t)², t≥ 0, ce R. Plot the phase portraits for this DE for all values of c. Use these phase portraits to plot a solution x(t) as a function of c.

Consider the function f(x)=2sin(π2(x−3))+4. State the amplitude A, period P, and midline. State the phase shift and vertical translation. In the full period [0, P], state the maximum and minimum y-values and their corresponding x-values. Hints for the maximum and minimum values of f(x): The maximum value of y=sin(x) is y=1 and the corresponding x values are x=π2 and multiples of 2π less than and more than this x value. You may want to solve π2(x−3)=π2. The minimum value of y=sin(x) is y=−1 and the corresponding x values are  x=3π2 and multiples of 2π less than and more than this x value. You may want to solve π2(x−3)=3π2. If you get a value for x that is less than 0, you could add multiples of P to get into the next cycles. If you get a value for x that is more than P, you could subtract multiples of P to get into the previous cycles.   For x in the interval [0, P], the maximum y-value and corresponding x-value is at:   x=        y=          For x in the interval [0,…

Find d2y/dx2 for the equation x=x3y2-3y3

y = cos(x),