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 = x

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

(Here P=1/x and Q=x^{2})

This is the required general solution of the given differential equation.

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