If c and d are arbitrary constants, then y=e^ 2 x ( 2 x+d 2 x) is the general solution of the differential equation

Step-by-step solution

y=e^ 2 x (c h 2 x+d h 2 x) Then, y^ =e^ 2 x (2 c h 2 x+2 d h 2 x+ 2 c h 2 x d 2 h 2 x) array r y^ =e^ 2 x [ h 2 x(2 c+d 2 )+2 h 2 x(2 d+ 2 c)] y^ =e^ 2 x [2 h 2 x(2 c+d 2 )+2 h 2 x (2 d+ 2 c)+ 2 (2 c+d 2 ) h 2 x + 2 (2 d+ 2 c) h 2 x] array Now, y^ -4 y^ +2 y=0