Solutions of Differential Equations of the First Order and First Degree
A differential equation of first degree and first order can be solved by following method .
1 . Inspection Method
If the differential equation ’ can be written as f [ f1 ( x , y ) d { f1 ( x , y )}] + φ [ f2 ( x , y ) d { f2 ( x , y )}] +… = 0 ] then each term can be integrated separately .
For this , remember the following results
2 . Variable Separable Method
If the equation can be reduced into the form f ( x ) dx + g ( y ) dy = 0 , we say that the variable have been separated . On integrating this reduced , form , we get ∫ f ( x ) dx + ∫ g ( y ) dy = C , = C , where
C is any arbitrary constant .