Multiply and reduce to lowest terms. Convert into a mixed number if necessary.
1 answer:
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As a Bernoulli equation:
Let
. The ODE becomes
![\dfrac{\mathrm d}{\mathrm dx}[x^6z]=-6x^4](https://tex.z-dn.net/?f=%5Cdfrac%7B%5Cmathrm%20d%7D%7B%5Cmathrm%20dx%7D%5Bx%5E6z%5D%3D-6x%5E4)
With
, we get
so the solution is
which is valid as long as the denominator is not zero, which is the case for all![x\neq\sqrt[5]{\dfrac{4131}{12}}](https://tex.z-dn.net/?f=x%5Cneq%5Csqrt%5B5%5D%7B%5Cdfrac%7B4131%7D%7B12%7D%7D)
.
Let
With
so the solution is
which is valid as long as the denominator is not zero, which is the case for all