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Which of the following are separable differential equations?
Which of the following are separable differential equations?A) (dy/dx) = x+y
B) xdy+1 = dx
C) dy/dx = xy/(1+x^(2))
D) (dy/dx)x+x^(2)y = x
E) y' = 2x-3y+1
F) dy/dx = xy
G) 2xydx+(x^(2)+1)dy = 0
H) dy/dx = x+y^(2)
I) dy/dx+yx^(2) = x^(2)
Theseparable differential equationsare:C)F)A separable differential equation is any equation that can be written in the form. The method of separation of variables is used to find thegeneral solutionto a separable differential equation.To determine which of the given differential equations are separable, we need to check if the variables can be separated on different sides of the equation.A)This is not separable because the variables x and y appear together on the right side.B)This is not separable.C)This is separable because we can rearrange the terms:D)This is not separable because the variables x and y appear together on both sides.E)This is not separable because the variables x and y appear together on the right side.F)This is separable because we can rearrange the terms:G)This is not separable because the variables x and y appear together on the left side.H)This is not separable because the variables x and y appear together on the right side.I)This is not separable because the variables x and y appear together on both sides.Therefore, the separable differential equations are:C)F) To know more aboutseparable differential equationsherebrainly.com/question/30611746#SPJ4...