Lesson Plan Math Class XII Ch 9  Differential Equations
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Board – CBSE 
CLASS –XII 
SUBJECT MATHEMATICS 
CHAPTER 9 : Differential
Equations 
 Knowledge of Trigonometry chapter 3 Class XII
 Knowledge of inverse trigonometric functions chapter 2 class XII
 Knowledge of Differentiation chapter 5 class XII
 Knowledge of Integration chapter 7 class XII
 Definition of Differential equations.
 Order and Degree of differential Equations.
 General and Particular solutions of Differential equations.
 Formation of differential equations whose general solution is given.
 Solution of differential equations by the method of separating the variables.
 Solution of homogeneous differential equations of first order and first degree.
 Solutions of Linear Differential equations of the following type where P and Q are the functions of x or constant , where P and Q are the functions of y or constant.
 Applications of Differential Equations in different field of mathematics.
S.No 
Explanation of the Topics 
1 
Differential
Equations : An equation which
involves the independent variable, dependent variable and
differential coefficients of dependent variable with respect to the
independent variable is called a differential equation. In dy/dx, the
dependent variable is y and independent variable is x. 
2 
Order
of the differential equations: It is defined as the
order of the highest order derivative of the dependent variable with respect
to the independent variable. 
3 
Degree
of Differential Equation: Degree of a differential
equation is defined if it is the polynomial equation in derivatives. Highest
power of the highest order derivative is called its degree. Before finding
the degree, the differential equation should be free made from radicals and
fractions. Order and degree(If defined) are always positive
integers. 
4 
General
Solution : The
solution which contains the arbitrary constants is called general solution. Particular
Solution : The
solution which is free from arbitrary constants is called a particular
solution. After giving the
knowledge of types of solutions teacher should explain the method of finding
the solutions and help the students in solving the problems given in the
NCERT book. 
5 
Now explain the method
of formation of differential equation whose general solution is
given by taking some problems from the text book. 
6 
Now explain
the method of solving the first order, first degree differential equations. These equations are of three types i)
Differential equations in which variables can be separable. ii)
Homogeneous Differential Equations.
iii) Linear
Differential Equations.
First of all
teacher should explain the method of solving the equations in which variables
can be separable. When the
differential equation is of the form f(x)dx = g(y)dy, then variables can be
separable. Such equations cab solved by integrating on both sides and the
solution is of the form:

7 
Equations
reducible to variable separable form: Differential equation of the form dy/dx = f(ax +
by + c) can be reduced to variable separable form by putting ax + by + c = v Teacher should explain
this method and problems related to it. 
8 
Homogeneous Differential Equations: If a first order first degree differential equation is expressible in the form Where f(x,
y) and g(x, y) are homogeneous functions of the same degree, then it is
called a homogeneous differential equation. Such types
of equations can be reduced to the variable separable form by the
substitution y = vx Teacher
should explain the complete method of solving such equations by solving some
problems.
Algorithm
a) Put y =
vx, and dy/dx = v + x dv/dx b) Shift v
to the RHS and separate the variables v and x
c)
Integrating on both sides to obtain the solution in terms of v and
x .
Replace
v by y/x in the solution obtained above so as to get the solution in x
and y form.
Sometimes a
homogeneous differential equation is expressible in the form Where f(x,
y) and g(x, y) are homogeneous functions of the same degree
In such a situation we
substitute x = vy and dx/dy = v + ydv/dy 
9 
Linear Differential Equations: A differential equation is linear if the dependent variable (y) and its derivative appear only in first degree. General form of Linear Differential equation is Algorithm a) Write the differential equation in the standard form dy/dx + Py = Q and then find P and Q b) Find integrating factor(IF) given by c) Multiply on both side of the equation by I.F. c) Integrating on both side with respect to x so that we get the solution in the form Sometimes the L.D.E. is of the form
and the solution becomes

10 
Teacher
should explain some applications of differential equations in different
fields of mathematics like growth and decay, Newton’s law of cooling,
coordinate geometry etc 
 After studying this lesson students should know the
 Differential equations their order , degree , arbitrary constants, general solutions and particular solutions.
 Students should also know the different methods of solving the differential equations like: variable separable method, homogeneous differential equation and linear differential equation.
 Review questions given by the teacher.
 Students can prepare a power point presentation on basic concepts and different methods of solving the differential equations.
 Solve NCERT problems with examples.
 Assignment sheet will be given as home work at the end of the topic.
 Separate sheets which will include questions of logical thinking and Higher order thinking skills will be given to the above average students.
 Class Test , Oral Test , worksheet and Assignments. can be made the part of assessment.
 Retest(s) will be conducted on the basis of the performance of the students in the test.
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