If `y=e^(-x)cosx`, then prove that `y_4+4y=0`.

If y=e^(-x)cos x, then prove that y_(4)+4y=0

If y=e^x(sinx+cosx) , then prove that, (d^2y)/(dx^2)-2dy/dx+2y=0

If y = e ^(-x) cos x then y _(4) =

If y = sin(2 cos^(-1)x) , then prove that (1 - x^2)(d^2y)/(dx) -x dy/dx + 4y = 0

If y=e^(2x)(ax+b), show that y_(2)-4y_(1)+4y=0

y=x^2 cosx then prove that x^2y_2-4xy_1+(x^2+6)y=0

If y=e^(2x)(a x+b) , show that y_2-4\ y_1+4\ y=0 .

IF y=e^(-x)(cosx+sinx) , show that , y_2+2y_1+2y=0 .

If e^(x) + e^(y) = e^(x + y) , then prove that (dy)/(dx) = (e^(x)(e^(y) - 1))/(e^(y)(e^(x) - 1)) or (dy)/(dx) + e^(y - x) = 0 .

If y=e^(ex)(ax+b), show that y^(2)-4y_(1)+4y=0