Please could someone help me with this diff equation - I have been trying multitudes of substitution and have not yielded any progress. Help will be very appreciated.
Thank you friends
This is a Riccati equation.
write it on the form : y' = P(x) +Q(x)*y +R(x)*y²
Let y = -z'/(z*R)
Compute y' in terms of z'', z', z
Bring back y' and y into y' = P(x) +Q(x)*y +R(x)*y²
This leads to a linear ODE (second order)
Solve it for z(x)
Bring back z' and z into y = -z'/(z*R) which leads to y(x)