For the primitive integral equation `y dx+y^2dy=xdy ; x in R ,y >0,y(1)=1,` then `y(-3)` is (a) 3 (b) 2 (c) 1 (d) 5

The solution of the primitive integral equation (x^2+y^2)dy=x y dx is y=y(x)dot If y(1)=1 and y(x_0)=e , then x_0 is

For y gt 0 and x in R, ydx + y^(2)dy = xdy where y = f(x). If f(1)=1, then the value of f(-3) is

The solution of the equation (x^2y+x^2)dx+y^2(x-1)dy=0 is given by

The solution of differential equation (2y+x y^3)dx+(x+x^2y^2)dy=0 is

Solve the differential equation: (1+y^2) + ( x - e^(tan^-1 y) ) dy/dx = 0

Find the solution of the differential equation: (d^2y)/dx^2 + 4(dy)/(dx)+3y=0

Find the particular solution of the differential equation (xe^(y/x)+y)dx=xdy, y = 1 when x = 1.

Let A B C be a triangle. Let A be the point (1,2),y=x be the perpendicular bisector of A B , and x-2y+1=0 be the angle bisector of /_C . If the equation of B C is given by a x+b y-5=0 , then the value of a+b is (a) 1 (b) 2 (c) 3 (d) 4

If x^2+y^2=t-1/t and x^4+y^4=t^2+1/t^2, then x^3y (dy)/(dx)= (a) 0 (b) 1 (c) -1 (d) non of these