If - 4 < x < 4 , then the general solution of the differential equation ^2 x d y d x -( 2 x) y= ^4 x is

Step-by-step solution

aligned & ^2 x d y d x - 2 x y= ^4 x & d y d x - 2 x ^2 x y= ^2 x aligned the above differential equation is in the form of. d y d x +p y=q , where p= - 2 x ^2 x and q= ^2 x Now, IF =e^ p d x =e^ - 2 x ^2 x d x Let aligned I & = - 2 x ^2 x d x= - 2 x 2 x ^2 x d x & = -2 2 x 2 x(1+ 2 x) d x aligned put 2 x=t-2 2 x d x=d t aligned I & = d t t(t+1) = d t t^2+t+ ( 1 2 )^2- ( 1 2 )^2 & = d t (t+ 1 2 )^2- ( 1 2 )^2 = | t t+1 | aligned