The general solution of the differential equation (1-x² ) d y d x +2 x y=x (1-x² )^ 1 2 is

Step-by-step solution

aligned & (1-x² ) d y d x +2 x y=x (1-x² )^ 1 2 & d y d x + 2 x y 1-x² = x (1-x² )^ 1 2 I.F. =& e^ 2 x 1-x² d x =e^ - -2 x 1-x² d x =e^ - (1-x² ) =e^ ( 1 1-x² ) = 1 1-x² aligned aligned ( 1 1-x² ) &= x (1-x² )^ 1 2 1 (1-x² ) d x &= -1 2 -2 x (1-x² )^ 3 / 2 d x= (- 1 2 ) (1-x² )^ - 1 2 (- 1 2 ) +c y ( 1 1-x² ) &= 1 1-x² +c y = 1-x² +c (1-x² ) aligned