When the number of independent variables is equal to the number of arbitrary constants The PDE obtained by eliminating the arbitrary constants is of?

A solution which contains the number of arbitrary constants is equal to the number of independent variables is called complete solution or complete integral. 2.

How many arbitrary constants must a general solution to a second-order differential equation have how are these constants determined?

two arbitrary constants
You have seen that Newton’s second law leads to second-order differential equations, and that the general solution of a second-order differential equation contains two arbitrary constants. The need for two arbitrary constants connects to everyday experience.

Is an equation which consists of one or more functions of one independent variable along with their derivatives?

ordinary differential equationAn ordinary differential equation (ODE) is an equation involving one independent variable; one or more dependent variables, each of which is a function of the independent variable; and ordinary derivatives of one or more of the dependent variables.

How many arbitrary constant are there in the particular solution of the differential equation dy dx y 0 )= 1?

Since there is no arbitrary constant in particular solution. ∴ (D) is correct answer. The number of arbitrary constants in the general solution of a differential equation of fourth order are: 0.

How many arbitrary constant are there in particular solution?

Number of arbitrary constants in the general solution of a differential equation is equal to the order of differential equation, while the number of arbitrary constants in a particular solution of a differential equation is always equal to $0$. Here the order of the differential equation is 2.

What is two or more equations involving the derivatives of two or more unknown functions of a single independent variable?

A partial differential equation (or briefly a PDE) is a mathematical equation that involves two or more independent variables, an unknown function (dependent on those variables), and partial derivatives of the unknown function with respect to the independent variables.