What is the solution for (dy)/(dt)=(4t^8)/(e+t^9) ?

The solution for (dy)/(dt)=(4t^8)/(e+t^9) is y= 4/9 ln(e+t^9)+c_{1}

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(dy)/(dt)=(4t^8)/(e+t^9)

\frac{d y}{d t} = \frac{4 t ^{8}}{e + t ^{9}}

y = \frac{4}{9} ln (e + t^{9}) + c_{1}

Solution steps

\frac{d y}{d t} = \frac{4 t ^{8}}{e + t ^{9}}

Substitute

\frac{d y}{d t}

with

y^{'} (t)

y^{^{'}} (t) = \frac{4 t ^{8}}{e + t ^{9}}

f^{^{'}} (x) = g (x)

then

f (x) = \int g (x) d x

y = \int \frac{4 t ^{8}}{e + t ^{9}} d t

\int \frac{4 t ^{8}}{e + t ^{9}} d t = \frac{4}{9} ln (e + t^{9}) + c_{1}

y = \frac{4}{9} ln (e + t^{9}) + c_{1}

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y^{^{'}} = e^{5 x} - 9 x

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\int_{0}^{r} r^{2} - x^{2} d x

What is the solution for (dy)/(dt)=(4t^8)/(e+t^9) ?
The solution for (dy)/(dt)=(4t^8)/(e+t^9) is y= 4/9 ln(e+t^9)+c_{1}