If x=logp and y=1/p ,then (a)(d^2y)/(...

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`

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Solve (d^2y)/(dx^2)=((dy)/(dx))^2

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

If y=xlog(x/(a+b x)),t h e nx^3(d^2y)/(dx^2)= (a) x(dy)/(dx)-y (b) (x(dy)/(dx)-y)^2 y(dy)/(dx)-x (d) (y(dy)/(dx)-x)^2

(d^2x)/(dy^2) equals: (1) ((d^2y)/(dx^2))^-1 (2) -((d^2y)/(dx^2))^-1 ((dy)/(dx))^-3 (3) -((d^2y)/(dx^2))^-1 ((dy)/(dx))^-2 (4) -((d^2y)/(dx^2))^-1 ((dy)/(dx))^3

(d^2x)/(dy^2) equals: (1.) ((d^2y)/(dx^2))^-1 (2) -((d^2y)/(dx^2)) ((dy)/(dx))^-3 (3) -((d^2y)/(dx^2))^-1 ((dy)/(dx))^-2 (4) -((d^2y)/(dx^2))^-1 ((dy)/(dx))^3

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

Which of the following differential equations has y=c_1e^x+c_2e^(-x) as the general solution? (A) (d^2y)/(dx^2)+y=0 (B) (d^2y)/(dx^2)-y=0 (C) (d^2y)/(dx^2)+1=0 (D) (d^2y)/(dx^2)-1=0

(d^2x)/(dy^2) equals: (1) ((d^2y)/(dx^2))^(-1) (2) -((d^2y)/(dx^2))^(-1)((dy)/(dx))^(-3) (3) ((d^2y)/(dx^2))^(-1)((dy)/(dx))^(-2) (4) -((d^2y)/(dx^2))^(-1)((dy)/(dx))^(-3)

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)

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