Notes on Differential equations, Cheat Sheet of Mathematics

Download Notes on Differential equations and more Cheat Sheet Mathematics in PDF only on Docsity!

7.6 METHODS OF SOLUTION OF DIFFERENTIAL EQUATIONS OF FIRST | ORDER AND FIRST DEGREE Depending upon the nature of the differential equations, various methods solving them are in practice. > shall study the following methods : 7.6.1 Method of Variables Separable Por this method, we rearrange the differential equation in the form, F (x) dx + G (y) dy=0 OR F (x) dx G (y) dy, where F (x) is function of x alone and G (y) ts a function of y alone. Then, integrating, we get, iF ( ydx +/G(y) dy = ¢ OR {F (x) dx= | G (y) dy +c, where ‘ce’ is aan arbitrary constant. Knowing the }F (x) dx 3 i ati d find the corresponding general solution. 5 Of 1 ion 1 e complete the integration an ypes of integration involved, w OO ] $$$ ee pte TDATIVE CYARDI Ec