if `y=ae^(x)+be^(-3x)+c`, then the value of `((d^(3)y)/(dx^(3))+2(d^(2)y)/(dx^(2)))/((dy)/(dx))` is

If y=log(1+sinx)," then "(d^(3)y)/(dx^(3))+(d^(2)y)/(dx^(2))(dy)/(dx)=

If y=log(1+cos x), prove that (d^(3)y)/(dx^(3))+(d^(2)y)/(dx^(2))(dy)/(dx)=0

y=log(1+cos x), prove that (d^(3)y)/(dx^(3))+(d^(2)y)/(dx^(2))*(dy)/(dx)=0

" If "2x=y^(1/3)+y^((-1)/(3))," then the value of "((x^(2)-1))/(y)(d^(2)y)/(dx^(2))+(x)/(y)(dy)/(dx)=

Show that (d ^(2)x)/( dy^2) =- ((d ^(2) y )/( dx ^(2))) ((dy)/(dx)) ^(-3)

If y=x^(3) then the value of ((d^(2)y)/(dx^(2)))/([1+((dy)/(dx))^(2)]^((3)/(2))) at the point (1, 1) is -

if x=2+t^(3),y=3t^(2)" ,then the value of n for which "(((d^(2)y)/(dx^(2))))/((dy)/(dx))^(n) is constant is

The degree of the differential equation (d^(3)y)/(dx^(3))+2((d^(2)y)/(dx^(2)))^(2)-(dy)/(dx)+y=0 is