Find the positive solutions of the system of equations `x^(x+y)=y^n and y^(x+y)= x^(2n). y^n`, where ` ngt0`

Find the solution of homogeneous system of equations: x -2y +z =0; x + y = z and 3x + 6y = 5z

Which of the following (x,y) pairs is the solution for the system of equations x + 2y = 4 and -2x + y = 7 ?

Which of the following (x,y) pairs is the solution for the system of equations x + 2y = 2 and -2x + y = 16 ?

Find the particular solution of the differential equation ; (x^2+x y)dy=(x^2+y^2)dx given that y=0\ w h e n\ x=1.

Find the particular solution of the differential equation (dy)/(dx)=(x y)/(x^2+y^2) given that y=1\ w h e n\ x=0.

If (x_(0), y_(0), z_(0)) is any solution of the system of equations 2x-y-z=1, -x-y+2z=1 and x-2y+z=2 , then the value of (x_(0)^(2)-y_(0)^(2)+1)/(z_(0)) (where, z_(0) ne 0 ) is

Find a particular solution of the differential equation: (x+y)dy+(x-y)dx=0; y=1\ w h e n\ x=1

Find the particular solution of the differential equation (dx)/(dy)+xcoty=2y + y^2cot y ,\ y!=0 given that x=0\ w h e n\ y=pi/2 .

Solve the following system of equations: 2/x+3/y=9/(x y),\ \ \ 4/x+9/y=(21)/(x y),\ \ where x!=0,\ y!=0

Let Y = y(x) be the solution of the differential equation ( dy ) /( dx) + 2y = f(x) , where f(x) = { {:(1, x in [0,1]),( 0, " Otherwise "):} IF y(0) =0 then y ((3)/(2)) is :