Differential Equations Chapter 9 Class 12 Basic concepts and formulas of differential equations chapter 9 class 12, method of solving homogeneous differential equations and linear differential equations. Differential equation An equation involving derivative of the dependent variable with respect to independent variable is called a differential equation. Differential equations are widely used in the field of Physics, Chemistry, Biology, Geology, Economics etc.  Examples of differential equations: \[\frac{dy}{dx}+y=5\]\[\frac{d^{4}y}{dx^{4}}+5\frac{d^{2}y}{dx^{2}}+ 3y=10\] In this chapter we will discuss the following points Basic concepts related to the differential equations. General and particular solutions of differential equations. Formation of differential equations. Method of solving Homogeneous Differential Equations Method of solving Linear Differential Equations . Some applications of differential equations in different areas. Special notations ...

Three Dimensional Geometry Class XII Chapter 11 Basic concepts and formulas of 3D-Geometry class XII chapter 11, Equations of line and plane in space, shortest distance between skew lines, angle between two lines and planes.   Introduction: It is that branch of mathematics in which we discuss the point, line and plane in the space.  We got a little introduction of 3 dimensional -Geometry in class 11 chapter 12. Here in class XII we make use of vector algebra in 3 dimensional - Geometry.  In this chapter we discuss the following points. Direction angles,  Direction cosines  Direction ratios.  Equation of line passing through one point, two point. Angle between two lines, parallel lines and perpendicular lines. Shortest distance between two lines. Collinearity of two lines. Equation of plane passing through  one point and through three points. Angle between two planes. Distance of the plane from the point. Angl...

Three Dimensional Geometry Basic concepts of three dimensional geometry class 11 , Distance formula , section formula, mid-point formula and centroid of triangle Introduction :  To locate the position of a point in a plane we need two intersecting mutually perpendicular lines in the plane.    These lines are called  coordinate axis  and the two points in this case are called the coordinates of the point with respect to the axis.   To locate the position of an object in a space we need three mutually perpendicular planes.  These planes are called three  coordinate planes .     Three numbers representing the three distances of an object from three coordinate planes are called the coordinates of the point on the object. So any point in space has three coordinates.   Coordinate axis and coordinate planes in three dimensional planes Coordinate axis in two dimensions divide the plane into four quadrants.    In three di...

Straight Lines Class 11 Chapter 09 Basic concepts of straight line chapter 9 standard XI, slope of the line, different forms of equation of lines and general equation of line.

Coordinate Geometry Class X Chapter 7 Basic formulas and complete explanation of coordinate geometry  of 10th standard. It includes distance formula, section formula, mid-point formula, area of triangle area of quadrilateral and centroid of triangle Introduction   It is that branch of mathematics in which we solve the geometrical problems algebraically. In coordinate geometry we combine geometry and algebra. To locate a point in the plane we use a system of two lines which are perpendicular to each other. This system is called the cartesian coordinate system    Cartesian coordinate system   In this system there are two lines which intersect each other at a point perpendicularly. Point of intersection of two lines is called Origin. Horizontal line is called x-axis and Vertical line is called y-axis. Numbers are written on both the axis on either side of the origin. On x-axis positive numbers are written on the right side o...