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

x(d^(2)y)/(dx^(2))+(dy)/(dx)+x=0

Which of the following differential equations has y = x as one of its particular solution? (A) (d^2y)/(dx^2)-x^2(dy)/(dx)+x y=x (B) (d^2y)/(dx^2)+x(dy)/(dx)+x y=x (C) (d^2y)/(dx^2)-x^2(dy)/(dx)+x y=0 (D) (d^2y)/(dx^2)+x(dy)/(dx)+x y=0

The differential equation representing the family of curves given by y=ae^(-3x)+b , where a and b are arbitrary constants, is a) (d^(2)y)/(dx^(2))+3(dy)/(dx)-2y=0 b) (d^(2)y)/(dx^(2))-3(dy)/(dx)=0 c) (d^(2)y)/(dx^(2))-3(dy)/(dx)-2y=0 d) (d^(2)y)/(dx^(2))+3(dy)/(dx)=0

((d^(2)y)/(dx^(2)))^(2) + cos ((dy)/(dx)) = 0

[" The differential equation of the family of curves "],[y=c_(1)x^(3)+(c_(2))/(x)" where "c_(1)" and "c_(2)" are arbitrary "],[" constants,is "],[" O "x^(2)(d^(2)y)/(dx^(2))-x(dy)/(dx)-3y=0],[" (x) "(d^(2)y)/(dx^(2))+x(dy)/(dx)+3y=0],[" (x) "(d^(2)y)/(dx^(2))+x(dy)/(dx)-3y=0],[" (x) "(d^(2)y)/(dx^(2))-x(dy)/(dx)+3y=0]

If y=cotx show that (d^2y)/(dx^2)+2y(dy)/(dx)=0 .

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

In which of the following differential equation degree is not defined? (a)(d^2y)/(dx^2)+3(dy/dx)^2=xlog((d^2y)/(dx^2)) (b)((d^2y)/(dx^2))^2+(dy/dx)^2=xsin((d^2y)/(dx^2)) (c)x=sin((dy/dx)-2y),|x|<1 (d)x-2y=log(dy/dx)