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

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- Jul 19th 2013, 05:12 PMDiademHelp with DE
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 - Jul 19th 2013, 06:35 PMHallsofIvyRe: Help with DE
That's a rather non-linear equation. There are NO general methods for solving such an equation. There are some methods for getting an approximate solution. Is that sufficient/

- Jul 20th 2013, 03:38 AMDiademRe: Help with DE
Nevermind

- Jul 20th 2013, 04:27 AMProve ItRe: Help with DE
- Jul 20th 2013, 08:41 AMJJacquelinRe: Help with DE
Hi !

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)

Compute z'

Bring back z' and z into y = -z'/(z*R) which leads to y(x)