hey I need to find out whether a few differential equations are separable, first order linear, both, or neither. one of the equations is y'+4y^2=0

Question

watchmath · Answer

non linear since we have a y^2 there and it is separable since we can rewrite as
dy/(-4y^2)=dt

anonymous · Answer

ok I understand the linear equation part, but not so much the separable part.

watchmath · Answer

what is your definition for separable differential eq.?

anonymous · Answer

an equations that has y'=f(x)g(y)

watchmath · Answer

ok, then y'=(-4)y^2 and you can take f(x)=-4 and g(y)=y^2

anonymous · Answer

ok thanks, and for first order linear just look for highest power of y?

anonymous · Answer

some of the equations have x's

watchmath · Answer

not the power of y but what is the highest derivative that you have
for example
y'''+xy'-x^3=e^x is linear of order 3

anonymous · Answer

ok thanks

anonymous · Answer

would y''+x^2y+z=0 be separable?