The solution of equations of the form dy dx = f ( y )

A differential equation of the form dy dx = f ( y ) https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429294402/968186b9-ffa4-4f2b-aa54-7fc58a604561/content/eq4537.tif"/> is initially rearranged to give dx = dy f ( y ) https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429294402/968186b9-ffa4-4f2b-aa54-7fc58a604561/content/eq4538.tif"/> and then the solution is obtained by direct integration, i.e. ∫ dx = ∫ dy f ( y ) https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429294402/968186b9-ffa4-4f2b-aa54-7fc58a604561/content/eq4539.tif"/>