Class 12 Maths Differential Equations First order Linear differential equations

First order Linear differential equations

A differential equation of the from  dy/dx + Py = Q

where, P and Q are constants or functions of x only, is known as a first order linear differential equation.

Example: Another form of first order linear differential equation can be dx/dy+ Px =Q

where, P and Q are constants or functions of y only, is known as a first order linear differential equation

Steps involved to solve first order linear differential equation:

(i) Write the given differential equation in the form dy/dx + Py = Q  ,  where P, Q are constants or functions of x only.

(ii) Find the Integrating Factor (I.F)

(iii) Write the solution of the given differential equation as

y (IF) =∫Q + IF. dx  + C

Problem:  Solve equation:     dy/dx + y/x = x2

Solution. The given differential equation is in the form of dy/dx + Py = Q

(Here P=1/x and Q=x2) This is the required general solution of the given differential equation.

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