Unit 8 calc differential equations

What is the difference between a general and particular solutions of differential equations?

General has a + C, particular you find C

How to find slope fields?

plug into equation and sketch the slope at each point

What is separation of variables?

when you separate the x and ys. Ex: dy/dx = 5xy = 1/y dy = 5x dx (integrate each side)

What is the equation for exponential growth and decay?

y = Pe^rt P - initial r - rate t - time (if dy/dx = ky then k would be the “rate”). Solutions will be in the form y = Ce^kt ( C is constant of integration)

What is the equation for Arc Length (rectangular)?

integral of sqrt (1 + f(‘x)²)