What is the solution for (dy)/(dt)+3/t y=3t^2y^2 ?

The solution for (dy)/(dt)+3/t y=3t^2y^2 is y= 1/(t^3(-3ln(t)+c_{1))}

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(dy)/(dt)+3/t y=3t^2y^2

\frac{d y}{d t} + \frac{3}{t} y = 3 t^{2} y^{2}

y = \frac{1}{t ^{3} ( - 3 ln ( t ) + c _{1} )}

Solution steps

\frac{d y}{d t} + \frac{3}{t} y = 3 t^{2} y^{2}

Solve Bernoulli ODE:

y = \frac{1}{t ^{3} ( - 3 ln ( t ) + c _{1} )}

y = \frac{1}{t ^{3} ( - 3 ln ( t ) + c _{1} )}

in v erse l a pl a ce \frac{5 s}{( s ^{2} + 1 ) ^{2}}

d er i v a t i v e 5 x^{2} - sin (π x)

y^{^{'}} + 4 y = e^{- 4 t}, y (0) = 2

d er i v a t i v e y = \frac{3 + csc ( x )}{7 - csc ( x )}

t an g e n t \frac{2 x}{( x ^{2} - 5 ) ^{3}}, at x = 0

What is the solution for (dy)/(dt)+3/t y=3t^2y^2 ?
The solution for (dy)/(dt)+3/t y=3t^2y^2 is y= 1/(t^3(-3ln(t)+c_{1))}