Lesson 12 of 18Article17 min
Differential Equations: Models of Change
A differential equation relates a function to its derivatives. Solving means finding the function(s) that satisfy the relation — often with an initial condition selecting one solution.
What a DE says
A differential equation relates a function to its derivatives. Solving means finding the function(s) that satisfy the relation — often with an initial condition selecting one solution.
Worked separable example
dy/dx = 2xy with y(0)=3. Separate: dy/y = 2x dx (y≠0). ln|y| = x² + C. y = A e^(x²). y(0)=3 → A=3 → y=3e^(x²).
Slope fields sketch the DE without solving — tiny segments with slope f(x,y) at each point reveal the family of solution curves.