`(d^2y)/(dx^2)+(dy)/(dx)=e^x`

If e^y(x+1)=1 . Show that (d^2y)/(dx^2)=((dy)/(dx))^2

Let y(x) be a function satisfying (d^(2)y)/(dx^(2))-(dy)/(dx)+e^(2x)=0 , y(0)= and y^(')(0)=1 . If maximum value of y(x) is y(alpha) , then integral part of 2alpha is……………..

If y=sin((log)_e x) , then x^2\ (d^2y)/(dx^2)+x(dy)/(dx) is equal to.......

If y= e ^(mcos ^(-1)x) ,then (1-x^(2) ) (d^(2)y)/(dx^(2)) -x(dy)/(dx)=

If y= x^(2) e^(x) ,then ( d^(2)y)/(dx^(2)) -(dy)/(dx) =

y = Ae^(x) + Be^(-2x) is a solution of the D.E. (d^(2)y)/(dx^(2) )+ (dy)/(dx) -2y = 0

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

x(d^(2)y)/(dx^(2))+(dy)/(dx)+x=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

for any differential function y= F (x) : the value of ( d^2 y) /( dx^2) +((dy)/(dx)) ^3 . (d^2 x)/( dy^2)