Solve the differential equation with the given initial condition. y' = y^6 - e^{3t}y^6, y(0) = 1 y = ((-5t + 5/3e^{3t}))^{(1/5)} - 0.108
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We can rewrite it as: $$\frac{1}{y^6} \frac{dy}{dt} = e^{3t y^6}$$ Now, we can integrate both sides with respect to $t$: $$\int \frac{1}{y^6} \frac{dy}{dt} dt = \int e^{3t y^6} dt$$ Let's make a substitution: $u = y^6$, so $\frac{du}{dt} = 6y^5 \frac{dy}{dt}$. Show more…
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