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The general solution to the differential equation
is:
where
is an arbitrary constant.
Solución

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Como
Mind Expander
This equation can be interpreted as a differential form that can potentially be simplified or solved using techniques from calculus. To make progress, observe that this is a homogeneous equation. Both sides can be manipulated to isolate
by rearranging:
Solving this could involve substitution or recognizing patterns, such as using polar coordinates.
One interesting approach is to consider the symmetry of the equation. Notice that if you switch
and
, the equation remains structurally similar. This symmetry can hint towards possible solutions, allowing us to look for answers in simple forms like
, where
is a constant. This thought experiment can often yield elegant solutions. Happy solving!

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