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A particularly hard nonlinear first order ordinary differential equation: $y(t)^n+a(t)\frac{dy(t)}{dt}=ba(t)$

I hope this is an appropriate place to post this question, however, I am stuck on solving an apparently simple ODE.

  I have checked numerous texts, references, software packages and colleagues before posting this...

$y(t)^n+a(t)\frac{dy(t)}{dt}=ba(t)$$$y(t)^n+a(t)\frac{dy(t)}{dt}=ba(t)$$

If the RHS had a $y$ term it would simply be Bernoulli's equation. Does the $n$ term prevent a solution?

A particularly hard nonlinear first order ordinary differential equation: $y(t)^n+a(t)\frac{dy(t)}{dt}=ba(t)$

I hope this is an appropriate place to post this question, however, I am stuck on solving an apparently simple ODE.

  I have checked numerous texts, references, software packages and colleagues before posting this...

$y(t)^n+a(t)\frac{dy(t)}{dt}=ba(t)$

If the RHS had a $y$ term it would simply be Bernoulli's equation. Does the $n$ term prevent a solution?

A nonlinear first order ordinary differential equation: $y(t)^n+a(t)\frac{dy(t)}{dt}=ba(t)$

I am stuck on solving an apparently simple ODE. I have checked numerous texts, references, software packages and colleagues before posting this...

$$y(t)^n+a(t)\frac{dy(t)}{dt}=ba(t)$$

If the RHS had a $y$ term it would simply be Bernoulli's equation. Does the $n$ term prevent a solution?

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j.c.
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A particularly hard nonlinear first order ordinary differential equation: $y(t)^n+a(t)\frac{dy(t)}{dt}=ba(t)$

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