Basic ODE
An equation involving derivatives of a function.
What is a differential equation?
A differential equation with one independent variable.
What is an ordinary differential equation?
The highest derivative determines this property.
What is the order?
A solution containing arbitrary constants.
What is a general solution?
Equation where variables can be separated.
What is a separable equation?
Equation of the form dy/dx + Py = Q.
What is a linear differential equation?
Equation involving nonlinear terms like y².
What is a nonlinear differential equation?
Equation that can be written as Mdx + Ndy = 0.
What is an exact differential equation?
Equation reducible to exact form using a special function.
What is an integrating factor equation?
Method used when variables can be separated.
What is separation of variables?
Method used for first-order linear equations.
What is the integrating factor method?
Model for population growth: dP/dt = kP.
What is exponential growth?
Model for cooling of objects.
What is Newton’s law of cooling?
Model for radioactive decay.
What is exponential decay?
quation where solution is a straight line.
What is a linear equation?