First-order nonlinear ordinary differential equation

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SUMMARY

The discussion centers on solving the first-order nonlinear ordinary differential equation given by A*(dT(x)/dx)(1873.382+2.2111T(x))=90457.5-2.149*10^-10*(T(x))^4, where A is a constant. The equation is identified as separable, allowing for integration to find the solution. The recommended approach involves rearranging the equation to isolate dT and dx, facilitating the integration process. This method is essential for obtaining the temperature function T(x) in relation to the variable x.

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sam_89
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hii,
how to solve this differential equation:

A*(dT(x)/dx)(1873.382+2.2111T(x))=90457.5-2.149*10^-10* (T(x))^4
where A is a constant

Thank you
 
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It's separable. You could try to integrate it that way:

[itex]A \frac{1873.382+2.2111T}{90457.5-2.149\times 10^{-10} \, T^{4}} \, dT = dx[/itex]
 
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