What is the solution for (3y2-t2y5)(dy)/(dt)+t2y4=0 ?

The solution for (3y2-t2y5)(dy)/(dt)+t2y4=0 is y=-4(-1/5 t-3/25 ln(-5t+3))+c_{1}

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(3y2-t2y5)(dy)/(dt)+t2y4=0

(3 y 2 - t 2 y 5) \frac{d y}{d t} + t 2 y 4 = 0

y = - 4 (- \frac{1}{5} t - \frac{3}{25} ln (- 5 t + 3)) + c_{1}

Solution steps

(3 y 2 - t 2 y 5) \frac{d y}{d t} + t 2 y 4 = 0

Substitute

\frac{d y}{d t}

with

y^{'} (t)

(3 y \cdot 2 - t \cdot 2 y \cdot 5) y^{^{'}} (t) + t \cdot 2 y \cdot 4 = 0

Isolate

y^{'} (t) : y^{'} (t) = - \frac{4 t}{3 - 5 t}

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

then

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

y = \int - \frac{4 t}{3 - 5 t} d t

\int - \frac{4 t}{3 - 5 t} d t = - 4 (- \frac{1}{5} t - \frac{3}{25} ln (- 5 t + 3)) + c_{1}

y = - 4 (- \frac{1}{5} t - \frac{3}{25} ln (- 5 t + 3)) + c_{1}

What is the solution for (3y2-t2y5)(dy)/(dt)+t2y4=0 ?
The solution for (3y2-t2y5)(dy)/(dt)+t2y4=0 is y=-4(-1/5 t-3/25 ln(-5t+3))+c_{1}