Differential Equations

The integral character ∫

Method for solving linear differential equations:

1. Put equation into standard form: dy/dx + f(x)y = g(x)
2. Find the integrating factor: u(x) which is equal to e^∫f(x)dx, so du/dx = u(x)f(x)
3. multiply the standard form by u(x): u(x)dy/dx + u(x)f(x)y = u(x)g(x)
4. use the product rule (udy/dx + ydu/dx = (u,y)d/dx) on the left side: d/dx(u(x),y(x)) = u(x)g(x)
5. integrate both sides, use sources such as table of integrals: u(x)y(x) = ∫u(x)g(x)dx
6. solve for y

Examples

• Falling Body with Air Resist