What is the solution for (xdy)/(dx)+y=-8xy^2,y(1)=5 ?

The solution for (xdy)/(dx)+y=-8xy^2,y(1)=5 is y= 1/(x(8ln(x)+c_{1))}

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(xdy)/(dx)+y=-8xy^2,y(1)=5

\frac{x d y}{d x} + y = - 8 x y^{2}, y (1) = 5

y = \frac{1}{x ( 8 ln ( x ) + c _{1} )}

Solution steps

\frac{x d y}{d x} + y = - 8 x y^{2}

Solve Bernoulli ODE:

y = \frac{1}{x ( 8 ln ( x ) + c _{1} )}

y = \frac{1}{x ( 8 ln ( x ) + c _{1} )}

f (x) = \frac{x}{4} arcsin (x)

x y^{^{'}} + y = x^{3}

\int \frac{x + 1}{x ^{2} + 2 x - 3} d x

\frac{\partial}{\partial x} (x^{3} + 8 y^{3} - 6 x y + 5)

x \to - 1 - lim (x^{3} - 3)

What is the solution for (xdy)/(dx)+y=-8xy^2,y(1)=5 ?
The solution for (xdy)/(dx)+y=-8xy^2,y(1)=5 is y= 1/(x(8ln(x)+c_{1))}