" 1."(d^(2)y)/(dx^(2))+4x=0

IF y=(1)/(1+x+x^(2)+x^(3)), then value of (d^(2)y)/(dx^(2)) at x=0 is

If y=(1)/(1+x+x^(2)+x^(3)) , then the value of (d^(2)y)/(dx^(2)) at x=0 is -

If y=log (x + sqrt(x^(2) + 1)) then show that, (x^(2) + 1) (d^(2)y)/(dx^(2)) + x (dy)/(dx)= 0

If x=log pandy=(1)/(p), then (a) (d^(2)y)/(dx^(2))-2p=0 (b) (d^(2)y)/(dx^(2))+y=0 (c) (d^(2)y)/(dx^(2))+(dy)/(dx)=0( d) (d^(2)y)/(dx^(2))-(dy)/(dx)=0

If y=sin^(-1)x , show that (1-x^(2))(d^(2)y)/(dx^(2))-xdy/dx=0 .

If y=asin^(-1)x , then show that : (1-x^(2))(d^(2)y)/(dx^(2))-xdy/dx=0

If y=cos^(-1)x , then show that : (1-x^(2))(d^(2)y)/(dx^(2))-xdy/dx=0

If y=e ^((alpha +1)x) be solution of differential equation (d ^(2)y)/(dx ^(2)) -4 (dy )/(dx) +4y=0, then alpha is:

If y=e ^((alpha +1)x) be solution of differential equation (d ^(2)y)/(dx ^(2)) -4 (dy )/(dx) +4y=0, then alpha is:

If y=a^(4x)tan^(-1)(x). FInd (d^(2)y)/(dx^(2))