Class 12 Differential Equations Notes has been updated according to the latest syllabus of 2080. It means the notes of differential equations chapter provided in this article contains all the new exercise that has recently been updated. Now you don’t need to go anywhere searching for the notes of this chapter because we are here to serve you.

## Chapter – 15

__Differential Equations__

An exact equation is a type of first-order differential equation that can be written in the form:The equation is said to be exact if there exists a function such that:.

In other words, and are the partial derivatives of some function with respect to and respectively: and .

If such a function exists, the solution to the differential equation can be found by integrating and appropriately, leading to an expression for equal to a constant..

## Class 12 Differential Equations Notes PDF

This PDF will provide the solutions of every question from the 4th exercise of class 12 differential equation chapter. If you want the notes of other exercises then you can choose the exercise from the button given above.

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### Exact Equations

A differential equation written in the form , where and are functions of or or both, is said to be exact if there exists a function such that ,i.e., when is an exact or a perfect differential.

i.e., when is an exact or a perfect differential.The differential equation is exact, since which gives,

latex xy = c $where is an arbitrary constant. But, the differential equation is not exact as it stands.It, however, becomes exact if we multiply both sides of it by , since, becomes .On integration, we have , where is an arbitrary constant as its solution.

An expression or factor such as is called an integrating factor (I.F.). Integrating factors may be found in several ways. But we shall focus our interest mainly on those cases in which can be found by simple observations or inspection. One should not forget that an equation may be exact by simply regrouping various terms of the equation.

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