# example:Riccati Transformation

**URL:** <https://community.wolfram.com/t/example-riccati-transformation/14409>\
**Category:** Questions\
**Created:** [July 11, 2019, 3:54pm UTC](https://community.wolfram.com/t/example-riccati-transformation/14409 "2019-07-11T15:54:10Z")\
**Posts on this page:** 7\
**Page:** 1

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**Author:** ![amraazo86](https://avatars.discourse-cdn.com/v4/letter/a/6a8cbe/32.png) [@amraazo86](https://community.wolfram.com/u/amraazo86)\
**Post date:** [July 11, 2019, 3:54pm UTC](https://community.wolfram.com/t/example-riccati-transformation/14409/1 "2019-07-11T15:54:10Z")

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i want to solve the following example to mthematica but i can’t to resove it .Can you helpme to do it in wolfram mathematica?The second question  
RICCATI TRANSFORMATION IN RED COLOR.  
fink you for your help.  
I’m waiting the answer.

[Questions.nb](https://community.wolfram.com/uploads/short-url/g2NHRw4eRUCcqTinFFYAmlfHA58.nb) (61.5 KB)

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**Author:** ![gianlucagorni](https://avatars.discourse-cdn.com/v4/letter/g/ec9cab/32.png) [@gianlucagorni](https://community.wolfram.com/u/gianlucagorni)\
**Post date:** [July 11, 2019, 4:35pm UTC](https://community.wolfram.com/t/example-riccati-transformation/14409/2 "2019-07-11T16:35:45Z")

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This is one way of making the transformation:

```
logarithmicDerivativeTransformation =
 y -> DSolveValue[{\[Eta][t] == y'[t]/y[t], y[0] == 1}, y, t]

```

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<div class="post-metadata">

**Author:** ![amraazo86](https://avatars.discourse-cdn.com/v4/letter/a/6a8cbe/32.png) [@amraazo86](https://community.wolfram.com/u/amraazo86)\
**Post date:** [July 11, 2019, 4:59pm UTC](https://community.wolfram.com/t/example-riccati-transformation/14409/3 "2019-07-11T16:59:19Z")

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Fink you i try to do it in mathematica now

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**Author:** ![amraazo86](https://avatars.discourse-cdn.com/v4/letter/a/6a8cbe/32.png) [@amraazo86](https://community.wolfram.com/u/amraazo86)\
**Post date:** [July 11, 2019, 5:12pm UTC](https://community.wolfram.com/t/example-riccati-transformation/14409/4 "2019-07-11T17:12:11Z")

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i find this result  
y → Function[{t}, ,Exp^-integral(0 to 1) [\etha][K[1]] dK[1]+Integral(from 1 to t)[\etha][K[1]] dK[1]]

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<div class="post-metadata">

**Author:** ![amraazo86](https://avatars.discourse-cdn.com/v4/letter/a/6a8cbe/32.png) [@amraazo86](https://community.wolfram.com/u/amraazo86)\
**Post date:** [July 11, 2019, 5:14pm UTC](https://community.wolfram.com/t/example-riccati-transformation/14409/5 "2019-07-11T17:14:45Z")

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now how can i do?

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<div class="post-metadata">

**Author:** ![gianlucagorni](https://avatars.discourse-cdn.com/v4/letter/g/ec9cab/32.png) [@gianlucagorni](https://community.wolfram.com/u/gianlucagorni)\
**Post date:** [July 11, 2019, 5:53pm UTC](https://community.wolfram.com/t/example-riccati-transformation/14409/6 "2019-07-11T17:53:42Z")

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It is a replacement rule. You apply it to a differential equation whose unknown function is `y`.

Yours looks like homework. You cannot ask people to do it all for you.

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<div class="post-metadata">

**Author:** ![amraazo86](https://avatars.discourse-cdn.com/v4/letter/a/6a8cbe/32.png) [@amraazo86](https://community.wolfram.com/u/amraazo86)\
**Post date:** [July 11, 2019, 6:22pm UTC](https://community.wolfram.com/t/example-riccati-transformation/14409/7 "2019-07-11T18:22:50Z")

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ok