Differential Equation:

Differential Equation:

A differential equation is an equation that involve one or more derivatives.

The order of differential equation is determined by the highest order derivative occur in the equation.

First-Order Differential Equation

A first-order differential equation is an equation of the form:

dy/dx=y =f(x,y)

Separable Differential Equations

A first-order differential equation can be solved by integration if it is possible to collect all y terms with dy and all
x terms with dx. That is if it is possible to write the equation in the form:

h(y) dy=g(x) dx
Then by integrating both sides of this equation
Then by integrating both sides of this equation
???h(y) dy?=???g(x) dx?
After completing the integrations, a general solution is obtain that define y as a function of x.
Example: Solve the differential equation:
dy/dx=(1+y) e^x
Solution:
dy/dx=(1+y) e^x
dy=(1+y) e^x dx
1/((1+y) ) dy=e^x dx
???1/((1+y) ) dy?=???e^x dx?
ln??(1+y)?=e^x+C (Where C represents the combined constants of integration)