What is the solution for (dy}{dt}=(4y)/5-\frac{y^2)/(120) ?

The solution for (dy}{dt}=(4y)/5-\frac{y^2)/(120) is y=-(96e^{(4t+4c_{1})/5})/(1-e^{(4(c_{1)+t))/5}}

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(dy}{dt}=(4y)/5-\frac{y^2)/(120)

\frac{d y}{d t} = \frac{4 y}{5} - \frac{y ^{2}}{120}

y = - \frac{96 e ^{\frac{4 t + 4 c _{1}}{5}}}{1 - e ^{\frac{4 ( c _{1} + t )}{5}}}

Solution steps

\frac{d y}{d t} = \frac{4 y}{5} - \frac{y ^{2}}{120}

Solve separable ODE:

y = - \frac{96 e ^{\frac{4 t + 4 c _{1}}{5}}}{1 - e ^{\frac{4 ( c _{1} + t )}{5}}}

y = - \frac{96 e ^{\frac{4 t + 4 c _{1}}{5}}}{1 - e ^{\frac{4 ( c _{1} + t )}{5}}}

(- 6, 0), (0, 1)

\int_{- 1}^{1} 1 + x^{2} d x

\int tan (x) sec (x) d x

y = arctan (ln (2) x^{4})

(- 3, 4), (4, 1)

What is the solution for (dy}{dt}=(4y)/5-\frac{y^2)/(120) ?
The solution for (dy}{dt}=(4y)/5-\frac{y^2)/(120) is y=-(96e^{(4t+4c_{1})/5})/(1-e^{(4(c_{1)+t))/5}}