Motion with Velocity and Acceleration

The velocity is  v= \(\frac{ds}{dt}\)

The acceleration is  a= \(\frac{dv}{dt}\) = \(\frac{ds^2}{dt^2}\)= v \(\frac{dv}{ds}\)

Differential Equations Families and Curves

Differential equation y’=ay has solution f(x)=ce^ax where c ϵ ℝ

Differential equation y’=ay +b has solution  f(x)=ce^ax – \(\frac{b}{a}\)

Exponential Growth and Decay

Separable Differential Equations

A separable differential equation is an equation that can be written in the form y’=f(x)g(y)

Example :  Newton’s Law of Cooling

\(\frac{dT}{dt}\)= k(T-T_a)