Solve for `x_1, x_2, x_3, x_4, x_5` where: `x_1+x_3=yx_2 , x_3+x_5=yx_4, x_5+x_2=yx_1, x_2+x_4=yx_3, x_4+x-1=yx_5` (where y is given parmameter)

Solve x + y = 5, yx = 1

Consider the system of equations x_1+x_(2)^(2)+x_(3)^(3)+x_(4)^(4)+x_(5)^(5)=5 and x_1+2x_2+3x_3+4x_4+5x_5=15 where x_1,x_2,x_3,x_4,x_5 are positive real numbers. Then numbers of (x_1,x_2,x_3,x_4,x_5) is ___________.

Consider the system of equations x_1+x_(2)^(2)+x_(3)^(3)+x_(4)^(4)+x_(5)^(5)=5 and x_1+2x_2+3x_3+4x_4+5x_5=15 where x_1,x_2,x_3,x_4,x_5 are positive real numbers. Then numbers of (x_1,x_2,x_3,x_4,x_5) is ___________.

Consider the system of equations x_1+x_(2)^(2)+x_(3)^(3)+x_(4)^(4)+x_(5)^(5)=5 and x_1+2x_2+3x_3+4x_4+5x_5=15 where x_1,x_2,x_3,x_4,x_5 are positive real numbers. Then numbers of (x_1,x_2,x_3,x_4,x_5) is ___________.

Solve for x and y:x^(2)+2x sin(xy)+1=0

solve for x and yx^(2)+2x sin(xy)+1=0

Solve: yx^(2)dx =e^(-x) dy

x ^ (2) yx ^ (3) (dy) / (dx) = y ^ (4) cos x

If y = x^x , prove that y_2 - y^-1 (y_1)^2 - yx^-1 = 0