Hello:

I have to solve the following differential equation as shown in the attachment

please help me how to solve this differential equation

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- November 4th 2012, 01:36 AMmatmmandifferential equation
**Hello:**

I have to solve the following differential equation as shown in the attachment

please help me how to solve this differential equation - November 4th 2012, 02:08 AMchiroRe: differential equation
Hey matmman.

Have you considered the Bernoulli solution?

Bernoulli differential equation - Wikipedia, the free encyclopedia - November 4th 2012, 02:11 AMProve ItRe: differential equation
- November 4th 2012, 02:12 AMJJacquelinRe: differential equation
Hi !

it is a Riccati ODE.

First, change the variable : t=exp(-x)

leading to dy/dt = -(y²/4)+(y/t)+1

Then let y= (1/4) (df/dt)(1/f) where f(t) is the new unknown function.

This leads to a linear second order ODE of the Bessel Kind.

Solve it for f(t) in termes of t*BeselI[1, t/2] and t*BesselK[1, t/2]

Then derivate it and bring f(t) and (df/dt) into y= 4(df/dt)*(1/f)

Finally, remplace t by exp(-x) - November 4th 2012, 02:13 AMProve ItRe: differential equation
Wolfram gets this...

- November 4th 2012, 02:46 AMJJacquelinRe: differential equation
Wolfram gives the result that you will obtain thanks to the method which was given in my preceeding post.

Note that t=sqrt(exp(-2x)). In the WolframAlpha formula, the denominator of the fraction is the function f(t) and the numerator is 4(df/dt). - November 4th 2012, 03:45 AMmatmmanRe: differential equation
**thanks for all**

can we solve this equation numerically by matlab using ode or bvp4c function - November 4th 2012, 10:29 PMmatmmanRe: differential equation
**hi JJacquelin:**

if we subsitute y by (1/4) (df/dt)(1/f) then how the function will be

what about dy/dt replace it by (d2f/dt2)(1/4f) and y^2 replace it by (df/dt)^2*(1/4)^2 - November 5th 2012, 01:17 AMJJacquelinRe: differential equation
Sorry, there was a typo :

y= 4 (df/dt)(1/f)

This was correctly written at the end of my post :

<< Then derivate it and bring f(t) and (df/dt) into y= 4(df/dt)*(1/f) >> - November 5th 2012, 03:35 AMmatmmanRe: differential equation
**please can you send send the solution in detial** - November 5th 2012, 07:31 AMJJacquelinRe: differential equation