1. Central University Of Kashmir
Tulmulla Campus, Ganderbal Kashmir
BT – 301
Linear differential
Equation and
Equations reducible to
linear form
Presented by: Sameem Makhdoomi
Enrollment no. 2124CUkmr09

2.  What Is a Linear Differential Equation.
 Steps to Solve Linear Differential Equation.
 Different forms of LDE.
 Examples on LDE.
 Equations reducible to the linear form.
 Examples on Bernoulli’s equation.
Contents

3. The linear differential equation is of the form dy/dx + Py = Q,
where P and Q are numeric constants or functions in x. It consists of a
y and a derivative of y. The differential is a first-order differentiation
and is called the first-order linear differential equation.
What Is a Linear Differential
Equation?

4. Steps to Solve Linear Differential
Equation
The following three simple steps are helpful to write the general
solutions of a linear differential equation.
Step - I: Simplify and write the given differential equation in the form
dy/dx + Py = Q
where P and Q are numeric constants or functions in x.
Step - II: Find the Integrating Factor of the linear differential equation
IF = e^∫P.dx
Step - III: Now we can write the solution of the linear differential
equation as follows.

5. Two
forms:

6. Example 1

8. Example 2

9. IF /

11. Example 3

15. This can be simplified to represent the following linear differential
equation.
dy/dx - y/x = 2x
Comparing this with the differential equation (dy/dx + Py = Q)
we have the values of P = -1/x and the value of Q = 2x.
Hence we have the integration factor as
IF = e^∫ (−1x)dx
IF = e^(-logx) = e^(logx^-1)= 1/x
Example 4 xdy -(y + 2x^2).dx = 0

16. Further, the solution of the differential equation is as
follows.
y.(1/x) = ∫ 2x.(1/x) dx + c
y/x = ∫ 2.dx + c
y/x = 2x + c
y = 2x^2 + xc -Ans

17. Equations reducible to the linear form (Bernoulli’s equation)
dx

18. Example 5

19. Example 6

20. Example 7

21. Thank you
Sameem Makhdoomi