What is the solution for (dy)/(dx)+3/x y=16y^3 ?

The solution for (dy)/(dx)+3/x y=16y^3 is y=sqrt(5/(x(32+5c_{1)x^5))},y=-sqrt(5/(x(32+5c_{1)x^5))}

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(dy)/(dx)+3/x y=16y^3

\frac{d y}{d x} + \frac{3}{x} y = 16 y^{3}

y = \frac{5}{x ( 32 + 5 c _{1} x ^{5} )}, y = - \frac{5}{x ( 32 + 5 c _{1} x ^{5} )}

Solution steps

\frac{d y}{d x} + \frac{3}{x} y = 16 y^{3}

Solve Bernoulli ODE:

y = \frac{5}{x ( 32 + 5 c _{1} x ^{5} )}, y = - \frac{5}{x ( 32 + 5 c _{1} x ^{5} )}

y = \frac{5}{x ( 32 + 5 c _{1} x ^{5} )}, y = - \frac{5}{x ( 32 + 5 c _{1} x ^{5} )}

\int_{4}^{7} \frac{x}{x ^{2} + 6 x + 13} d x

f (x) = 2 x^{2} + 2 x, at x = - 3

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What is the solution for (dy)/(dx)+3/x y=16y^3 ?
The solution for (dy)/(dx)+3/x y=16y^3 is y=sqrt(5/(x(32+5c_{1)x^5))},y=-sqrt(5/(x(32+5c_{1)x^5))}