\frac{dy}{dt} = \frac{1}{4t^2} + \frac{1}{2} + \frac{y}{2t} - \frac{\sqrt{1+4ty}}{2t}
It looks better this way...
Using v = \frac{1}{4t^2} + \frac{y}{t}
I can reduce this equation to the following:
\frac{dv}{dt} = \frac{1}{2t} - \frac{1}{8t^3} - \frac{v}{2t} -...
I can separate the rewrite the equation to look like:
dy/dt = 1/2 - 1/2*y/t + [1/(4t^2) + y/t] - [1/(4t^2) + y/t]^1/2
so if I substitute v = [1/(4t^2) + y/t] I get
dy/dt = 1/2 - 1/2*y/t + v - v^1/2
after more re-arranging i then get
dy/dt = 1/2 + 1/(8t^2) + v/2 - v^(1/2)
and dv/dt =...
Any help with solving this first-order nonlinear ODE would be greatly appreciated! I do believe that an explicit solution exists.
Homework Statement
dy/dt = 1/(4t^2) + 1/2 + 1/2*y/t - 1/(2t)*((1+4ty)^(1/2))
I was led to believe that it could be solved by turning it into a linear...