Test: First Order Nonlinear PDE - Civil Engineering (CE) MCQ

Equations of the form, Pp + Qq = R are known as Lagrange’s linear equations, named after Franco-Italian mathematician, Joseph-Louis Lagrange (1736-1813).

Equations of the form, z = px + qy + f(p, q) are known as Clairaut’s partial differential equations, named after the Swiss mathematician, A. C. Clairaut (1713-1765).

There are 2 types of Iterative methods, (i) Interpolation methods (or Bracketing methods) and (ii) Extrapolation methods (or Open-end methods).

The following are the different standard methods used in finding the solution of a differential equation:

• Variable Separable
• Homogenous Equation
• Non-homogenous Equation reducible to Homogenous Equation
• Exact Differential Equation
• Non-exact Differential Equation that can be made exact with the help of integrating factors
• Linear First Order Equation
• Bernoulli’s Equation

For a differential equation to be linear the dependent variable should be of first degree. Since in equation x+x²=0, x² is not a first power, it is not an example of linear differential equation.

A solution of a differential equation is any function which satisfies the equation, i.e., reduces it to an identity. A solution is also known as integral or primitive.

The solution of a partial differential equation obtained by eliminating the arbitrary constants is called a general solution.

A differential equation is said to have a singular solution if in all points in the domain of the equation the uniqueness of the solution is violated. Hence, this solution cannot be obtained from the general solution.

A solution which does not contain any arbitrary constants is called a general solution whereas a particular solution is derived by substituting particular values to the arbitrary constants in this solution.

Concept:

For solving first order, first-degree differential equations always first inspect with variable separation method.

Calculation:

Given the differential equation is,

Where A is a constant.