y^2+5y=36/y^2+5y

Solution for y^2+5y=36/y^2+5y equation:

D( y )

y^2 = 0

y^2 = 0

y^2 = 0

1*y^2 = 0 // : 1

y^2 = 0

y = 0

y in (-oo:0) U (0:+oo)

y^2+5*y = 5*y+36/(y^2) // - 5*y+36/(y^2)

y^2+5*y-(5*y)-(36/(y^2)) = 0

y^2+5*y-5*y-36*y^-2 = 0

y^2-36*y^-2 = 0

t_1 = y^2

1*t_1^1-36*t_1^-1 = 0

1*t_1^1-36*t_1^-1 = 0

(1*t_1^2-36*t_1^0)/(t_1^1) = 0 // * t_1^2

t_1^1*(1*t_1^2-36*t_1^0) = 0

t_1^1

t_1^2-36 = 0

t_1^2-36 = 0

DELTA = 0^2-(-36*1*4)

DELTA = 144

DELTA > 0

t_1 = (144^(1/2)+0)/(1*2) or t_1 = (0-144^(1/2))/(1*2)

t_1 = 6 or t_1 = -6

t_1 in { -6, 6} 

t_1 = -6

y^2+6 = 0

1*y^2 = -6 // : 1

y^2 = -6

t_1 = 6

y^2-6 = 0

1*y^2 = 6 // : 1

y^2 = 6

y^2 = 6 // ^ 1/2

abs(y) = 6^(1/2)

y = 6^(1/2) or y = -6^(1/2)

y in { 6^(1/2), -6^(1/2) }