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.Â
 Chapter – 15 Â
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
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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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