Find the number of point `(x ,y)` having integral coordinates satisfying the condition `x^2+y^2<25`

Find the number of positive integral solutions satisfying the equation (x_1+x_2+x_3)(y_1+y_2)=77.

Find the number of positive integral solutions of x y z=21600.

Find the number of pairs of integer (x , y) that satisfy the following two equations: {cos(x y)=x and tan(x y)=y (a) 1 (b) 2 (c) 4 (d) 6

Find the number of positive integral solutions of the equation x+y+z=12.

Find the number of positive integreal solutions of ( pairs of positive integers satisfying ) x^2 - y^2 = 353702 .

The number of points P(x , y) lying inside or on the circle x^2+y^2=9 and satisfying the equation tan^4x+cot^4x+2=4sin^2y is______

For each of the differential equations in find the particular solution satisfying the given condition : x^(2)dy+(xy+y^(2))dx=0,y=1 when x=1

For each of the differential equations in find the particular solution satisfying the given condition : [xsin^(2)((y)/(x))-y]dx+xdy=0,y=(pi)/(2) when x=1

For each of the differential equations in find the particular solution satisfying the given condition : 2xy+y^(2)-2x^(2)(dy)/(dx)=0,y=2 when x=1