What is the solution for (dy)/(dx)-y/x =-5/2 x^2y^3 ?

The solution for (dy)/(dx)-y/x =-5/2 x^2y^3 is y= x/(sqrt(x^5+c_{1))},y=-x/(sqrt(x^5+c_{1))}

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(dy)/(dx)-y/x =-5/2 x^2y^3

\frac{d y}{d x} - \frac{y}{x} = - \frac{5}{2} x^{2} y^{3}

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

Solution steps

\frac{d y}{d x} - \frac{y}{x} = - \frac{5}{2} x^{2} y^{3}

Solve Bernoulli ODE:

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

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

What is the solution for (dy)/(dx)-y/x =-5/2 x^2y^3 ?
The solution for (dy)/(dx)-y/x =-5/2 x^2y^3 is y= x/(sqrt(x^5+c_{1))},y=-x/(sqrt(x^5+c_{1))}