y' = (2x) / y+(x^2)y y(0) = -2
i realize this is sort of algebra prob, but i cant seem to separate x's from y's..
Mistake in line above. It looks like you are trying to say that 2x/(1 + x^2) = 2x/1 + 2x/x^2.Please check my work thanks alot..
find solution in explicit form:
y' = (2x) / y+(x^2)y initial conditions: y(0) = -2
dy/dx = 2x/y(1+x^2)
y dy = 2x + (2/x) dx
integrate both sides...
(1/2)y^2 = x^2 + 2ln|x| + c
y^2 = 2x^2 + 4ln|x| + 2c
y = root [2x^2 + 4ln|x| + c]
-2 = root [2(0)^2 + 4ln|0| + c]
-2 = (root 4) + c
c = -4 (i am reasong that root c is same as c because whether its root c or just c, both are still constants.. right?)
so my solution is:
y = root [2x^2 + 4ln|x| -4]