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 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

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

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

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)

For each of the following differential equations verify that the accompanying functions a solution. (i) x(dy)/(dx)=y => y=a x (ii) x+y(dy)/(dx)=0 => y=+-sqrt(a^2-x^2) (iii) x(dy)/(dx)y+y^2 => y=a/(x+a) (iv) x^3(d^2y)/(dx^2)=1 => y=a x+b+1/(2x) (v) y=((dy)/(dx))^2 => y=1/4(x+-a)^2

Verity that y=a/x+b is a solution of the differential equation (d^2y)/(dx^2)+2/x((dy)/(dx))=0.

The degree of the potential equation ((d^(2)y)/(dx^(2)))^(2)+((dy)/(dx))^(2)=x sin ((dy)/(dx))"is

Show that y=e^(2x) is a solution of differential equation (d^(2)y)/(dx^(2))+(dy)/(dx)-6y=0

Verify that y=ae^(3x)+be^(-x) is a solution of differential equation (d^2y)/(dx^2)-2(dy)/(dx)-3y=0

Find the order and degree of the following differential equations. i) (dy)/(dx)+y=1/((dy)/(dx)) , ii) e^(e^(3)y)/(dx^(3))-x(d^(2)y)/(dx^(2))+y=0 , iii) sin^(-1)(dy)/(dx)=x+y , iv) log_(e)(dy)/(dx)=ax+by v) y(d^(2)y)/(dx^(2))+x((dy)/(dx))^(2)-4y(dy)/(dx)=0