If `y^2=P(x)`, then `2d/dx(y^3(d^2y/dx^2))`

If y^2=a x^2+b x+c ,then y^3(d^2y)/(dx^2) is (a)a constant (b)a function of x only (c)a function of y only (d)a function of xa n dy

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

If y=2x^(n+1)+3xn ,then x^2d^2y/dx^2 is

If y^3-y=2x ,t h e n(x^2-1/(27))(d^2y)/(dx^2)+x(dy)/d= y b. y/3 c. y/9 d. y/(27)

If y=((alphax+beta)/(gammax+delta)), then 2(dy)/(dx).(d^(3)y)/(dx^(3)) is

Consider the family of all circles whose centers lie on the straight line y=x . If this family of circles is represented by the differential equation P y^(primeprime)+Q y^(prime)+1=0, where P ,Q are functions of x , y and y^(prime)(h e r ey^(prime)=(dy)/(dx),y^=(d^2y)/(dx^2)), then which of the following statements is (are) true? (a) P=y+x (b) P=y-x (c) P+Q=1-x+y+y^(prime)+(y^(prime))^2 (d) P-Q=x+y-y^(prime)-(y^(prime))^2

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

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)

(a+bx)e^(y/x)=x , Prove that x^3(d^2y)/(dx^2)=(x(dy)/(dx)-y)^2