General and particular solution of differential equation examples

The general solution of the differential equation is of the form y = ax + b, but the particular solution of the differential equation can be y = 3x + 4, y = 5x + 7, y = 2x + 1.

1. What is general solution of differential equation with example?
2. What is a general solution of a differential solution?
3. How do you find the general solution of an exact differential equation?
4. What is particular solution of equation?

What is general solution of differential equation with example?

Geometrically, the general solution represents an n-parameter family of curves. For example, the general solution of the differential equation dy/dx = 8x² which is found to be y = x³ + C, where c is considered as an arbitrary constant, represents a one-parameter family of curves as shown in the figure given below.

What is a general solution of a differential solution?

A solution of a differential equation is an expression for the dependent variable in terms of the independent one(s) which satisfies the relation. The general solution includes all possible solutions and typically includes arbitrary constants (in the case of an ODE) or arbitrary functions (in the case of a PDE.)

How do you find the general solution of an exact differential equation?

u_x(x, y) = p(x, y) and u_y (x, y) = Q(x, y); Therefore, the general solution of the equation is u(x, y) = C. Where “C” is an arbitrary constant.

What is particular solution of equation?

: the solution of a differential equation obtained by assigning particular values to the arbitrary constants in the general solution.