Sketch slope fields

Consider a slope field for the clipper circuit maintaining the output signal amplitude between [Amax, Amin]

The solution curve passes through origin for the given circuit. What is the value of [Amax, Amin]?

The fox and rabbit follow the predator-prey relationship in the forest. The population growth for both species is represented by Lotka-Volterra set of differential equation,

Rabbit :                    where a=0.4 and b=0.05

Fox :                              where c=0.2 and d= 0.005

 ‘a’ is the growth rate of rabbit population and ‘b’ is predation rate. Factor ‘c’ represents the mortality rate of fox and ‘d’ as growth of fox with predation. 

Which is of the following slope fields plot represents the variation of fox population with rabbit population if the initial population of rabbit and fox is 20 and 4 respectively?

Consider a differential equation, 

If the solution curve passes through origin, for x>3,  y(x) will tend to:

Consider a differential equation,

And, slope field plotted for same is given below,

What is the value of ‘a’?

The differential equation for system is given as,

Which of the following slope field plot represent the given equation?

In Peru, the population growing logistically has exceeded the carrying capacity due to rise in birth rate. If the population is 4.5 million at present, which slope field and solution curve represent the Peru population trend?

The solution of the given differential equation is an ellipse intersecting at point

Which of the following represent slope field plot for the given ellipse?

A pneumatic system is represented by differential equation given as:

Which slope field represent the solution curve for above DE if y(0)=1.5 and value of y(6)?

U-grape mobile manufacturing has launched a new smartphone with dual Bluetooth module. The smartphone is a hit with initial sales of 1 million pieces and sales department has predicted the sales to grow logistically and saturate eventually. Below is the slope field representation of smartphone sales.

What is the number of units sold just before saturation?

The velocity (v) car riding uphill is given as,

where, ‘t’ is time. If car starts acceleration at point of ascend with initial velocity v(0) of 25kmph, for how long the car need to accelerate to climb the hill?

The solution to the given differential equation is an equation of polygon intersecting the y axis at 2 units.

What is the area of polygon?

The concentration of product is increase as the chemical reaction proceeds. During the reaction, the heating plate was turned after ‘tx’ minutes, and reaction rate decreases. The product concentration rate is given as,

If the concentration of product at start of reaction is 0, what is value of ‘tx’?

Slope fields for two differential equations dydt,dxdt are represented below.

Figure 1 Slope Field for dx/dt

                                                                                                    Figure 2 Slope Field for dy/dt

The differential equation dy/dx is given by,

Solution for a differential equation is given as,

             and                  y(0)=0

Which slope field correctly represents the differential equation?

Given below is the RC circuit and slope field for the capacitor voltage Vc(t) for the the circuit.

If V(t)=0  for all t, Vc(0)=6V.What is the capacitor voltage after two time constant and differential equation for same?