Question

Define general solution and particular solution of a differential equation.

Answer 1

Answer:

Hope this helps.

The general solution describes all solutions to the differential equation without any boundary conditions.

A particular solution is the one solution that also satisfies the boundary conditions.

e.g.

Equation:  dy/dx = 2x

There are infinitely many solutions.  They are all described by:

y = x² + c,  where c is a constant.

This is the general solution for this equation.

Boundary condition:  When x = 1, y = 5.

The only solution that satisfies the equation AND this boundary condition is:

y = x² + 4

This is the particular solution for this equation with this boundary condition.