Questions from General Calculus

Q: Verify that y = -t cos t = t is a

Verify that y = -t cos t = t is a solution of the initial value problem

Q: Which of the following functions are solutions of the differential equation /

Which of the following functions are solutions of the differential equation /

Q: (a) Show that every member of the family of functions

(a) Show that every member of the family of functions y = (In x + C)/x is a solution of the differential equation / (b) Illustrate part (a) by graphing several members of the family of solutions on a...

Q: (a) What can you say about a solution of the

(a) What can you say about a solution of the equation y’ = -y2 just by looking at the differential equation? (b) Verify that all members of the family /are solutions of the equation...

Q: (a) What can you say about the graph of a

(a) What can you say about the graph of a solution of the equation / when x is close to 0? What if x is large? (b) Verify that all members of the family / are solutions of the differential equation /...

Q: A population is modeled by the differential equation / (

A population is modeled by the differential equation (a) For what values of P is the population increasing? (b) For what values of P is the population decreasing? (c) What are the equilibrium solution...

Q: The Fitzhugh-Nagumo model for the electrical impulse in a neuron

The Fitzhugh-Nagumo model for the electrical impulse in a neuron states that, in the absence of relaxation effects, the electrical potential in a neuron v(t) obeys the differential equation where a is...

Q: Explain why the functions with the given graphs can’t be solutions of

Explain why the functions with the given graphs can’t be solutions of the differential equation

Q: The function with the given graph is a solution of one of

The function with the given graph is a solution of one of the following differential equations. Decide which is the correct equation and justify your answer.

Q: Match the differential equations with the solution graphs labeled I–IV

Match the differential equations with the solution graphs labeled I–IV. Give reasons for your choices.