If z= (y+a x)+ y-a x , then z_ x x -a^2 z_ y y is equal to

Step-by-step solution

We have, z= (y+a x)+ y-a x z_x=a ^2(y+a x)+ (-a) 2 y-a x z_ x x =2 a^2 ^2(y+a x) (y+a x)- a^2 4 (y-a x)^ -3 / 2 and z_y= ^2(y+a x)+ 1 2 y-a x z_ y y =2 ^2(y+a x) (y+a x)- 1 4 (y-a x)^ -3 / 2 aligned & a^2 z_ y y =2 a^2 ^2(y+a x) (y+a x) - a^2 4 (y-a x)^ -3 / 2 aligned Now, z_ x x -a^2 z_ y y =0