Sample Material of Online Coaching For SSC CGL (Tier - 2) - Differential Equation
Sample Material SSC CGL TIER-2 Online Coaching
Numerical Aptitude (Chapter: Differential Equation)
Differential Equation
An equation containing and independent variable, dependent variable and
differential coefficient of dependent variable with respect to independent
variable is called a differential equation:
e.g. d3 y/dx3 -3(d2 y/dx2) +3dy/dx
-y= sin 2x
Types of Differential Equations
(i) Ordinary differential equation (only one independent variable) e.g. dy/dx = y
(ii) Partial differential equation (two or more independent variables) e.g. x(dz/dx) + y(dz/dy)+z = 0
Order of a Differential Equations
The order of a differential equation is the order of the highest order
derivative appearing in the equation.
e.g. :d2 y/dx2 -3(dy/dx) + 2y =e order =
2
Degree of a Differential Equation
The degree of a differential equation is the exponent of highest order derivative, when differential coefficient are made free from radicals and factions.
[1+{dy/dx}2 ]3 = 9 {d2 y/dx2 }3, degree = 2
Primitive or Solution of a Differential Equation
A primitive or solution of a differential equation is a functional relation between x and y which is free from derivatives and this relation on substitution satisfies the differential equation.
General Solution:
It is the solution which contains the number of arbitrary constants equal to the order of the differential equation.
Particular Solution:
A particular solution of differential equation is a solution obtained from the general solution by giving particular values to the arbitary constant.
Note:
In exceptional case a relation containing n arbitrary constants may give rise to a differential equation of order less than n.Formation of Differential Equation
Suppose
y = A e2x + Be–2x, eliminating arbitrary constant A and B i.e. and dy/dx = 2Ae2x - 2Be-2x
d2y/dx2 = 4Ae2x +4Be-2x =4y
i.e. d2y/dx2 -4y= 0
Solution of Ordinary Differential Equations of the First Order and First
Degree An ordinary differential equation of the first order and the first degree
is of the form
M+M (dx/dy )= 0
or Mdx + Ndy = 0
Where M and N are function of x and y or constant. The general solution of such
equation will contain only one arbitary constant.
:: Home Assignment for Practice ::
1.
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4. The slope of a curve at any point is the reciprocal of twice the ordinate at the point and it passes through the point (4,3). Then the equation of the curve is:
(a) x2 = y + 5
(b) y2 = x – 5
(c) y2 = x + 5
(d) x2 = y – 5
5.