Differential Equations

A population P satisfies dP/dt = 0.04P and has an initial population of 500. Find P(t) and determine the population after 10 years.

Classify the differential equation y'' + 4y' - 5y = 0 by order and linearity.

For the autonomous differential equation dy/dt = y(4 - y), find the equilibrium solutions and determine whether each equilibrium is stable or unstable.

Solve the differential equation dy/dx = 4x^3.

Solve the first-order linear differential equation y' + 2y = 6.

Solve the initial-value problem dy/dx = 2xy with y(0) = 3.

Solve the nonhomogeneous differential equation y'' - y = 6.

Solve the second-order differential equation y'' - 5y' + 6y = 0.

Solve the second-order differential equation y'' - 6y' + 9y = 0.

Solve the separable differential equation dy/dx = xy.