`y=ae^(-1/x)+b` is a solution of `dy/dx=y/x^2`,then (a)`ainR` (b)`b=0` (c)`b=1` (d)`a` takes finite number of values

The system of equations -2x+y+z=a , x-2y+z=b , x+y-2z=c , has: (a)no solution if a+b+c!=0 (b)unique solution if a+b+c=0 (c)infinite number of solutions if a+b+c=0 (d)none of these

Show that \ y=A e^(B x) is as solution of the differential equation (d^2y)/(dx^2)=1/y((dy)/(dx))^2dot

xy=( x+y )^n and dy/dx = y/x then n= 1 b. 2 c. 3 d. 4

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

If the solution of the differential equation (dy)/(dx)-y=1-e^(-x) and y(0)=y_0 has a finite value, when x->oo, then the value of |2/(y_0)| is__

STATEMENT-1 : y = e^(x) is a particular solution of (dy)/(dx) = y . STATEMENT-2 : The differential equation representing family of curve y = a cos omega t + b sin omega t , where a and b are parameters, is (d^(2)y)/(dt^(2)) - omega^(2) y = 0 . STATEMENT-3 : y = (1)/(2)x^(3)+c_(1)x+c_(2) is a general solution of (d^(2)y)/(dx^(2)) = 3x .

40.The number of solutions of 3^(x+y)=243 and 243^(x-y)=3 is: (a) 0 (b) 1 (c) 2 (d) infinite

Solution of ((x+y-a)/(x+y-b))((dy)/(dx))=((x+y+a)/(x+y+b))

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

If y(x) is solution of x(dy)/(dx)+2y=x^(2), y(1)=1 then value of y(1/2)= (a) -(49)/(16) (b) (49)/(16) (c) (45)/(8) (d) -(45)/(8)