First Order Differential Equations

What is plan A to handle first order differential equations?

Seperate the variables, e.g:
f(y) dy/dx = g(x)

What is plan B to handle first order differential equations?

Aim for the standard form of:
dy/dx + f(x)y = g(x)

How is the integrating factor calculated for plan B of handling first order differential equations?

e^(int( f(x) ) dx)

How are coupled differential equations handled?

• Make the variable to be eliminated the subject of the relevant differential equation
• Differentiate this equation
• Use both relationships as a double substitution into the other equations

How do you use plan A to find the particular solutions (A and B) values?

• If boundary conditions are known, get a complete set of results and use these to find unknown constants for the first variable
• Substitute the particular solution and it's derivative back into the initial equation to find the particular equation for the second variable

How do you use plan B to find the particular solutions (A and B) values?

• If boundary conditions not known prior to general solution of second variable being asked, sun general solution and its derivative back into initial substitution to find find particular solution for second variable

How are differential equations generally derived?

dx/dt = (dx/dt)in - (dx/dt)out