Hi guys I am really stuck on this differential equation can anyone help?
dy/dt = (t^2 + y^2) / (3ty)
condition - y=1 and t=2
Thank you in advance
This is an example of A DE with Homogeneous Coefficients
ie it can be written in the form dy/dt = f(y/t)
dy/dt = 1/3 t/y + 1/3 y/t
Let z= y/t
tz = y
and z + tdz/dt = dy/dt
z + t dz/dt = 1/(3z) + 1/3z
tdz/dt = 1/(3z) - 2z/3
you now have a separable equation I'll let you go from here
No it's not separable--- the problem being the t^2 + y^2 term.
Typically when fns of y and t are multiplied or divided the eqn can be separated -- when there is addition of fns of y and t you usually cannot separate them.
Go ahead and try but you'll soon see the eqn won't separate