What is the solution for xy^3dx+ex^2dy=0 ?

The solution for xy^3dx+ex^2dy=0 is y=sqrt(-e/(2(-ln(x)+c_{1)))},y=-sqrt(-e/(2(-ln(x)+c_{1)))}

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xy^3dx+ex^2dy=0

x y^{3} d x + e x^{2} d y = 0

y = - \frac{e}{2 ( - ln ( x ) + c _{1} )}, y = - - \frac{e}{2 ( - ln ( x ) + c _{1} )}

Solution steps

x y^{3} d x + e x^{2} d y = 0

Solve separable ODE:

y = - \frac{e}{2 ( - ln ( x ) + c _{1} )}, y = - - \frac{e}{2 ( - ln ( x ) + c _{1} )}

y = - \frac{e}{2 ( - ln ( x ) + c _{1} )}, y = - - \frac{e}{2 ( - ln ( x ) + c _{1} )}

\frac{d y}{d x} = \frac{x + x y}{1 + x ^{2}}

\frac{d y}{d x} - \frac{y}{4} = 0

y^{^{'}} - y = 0, y (0) = cosh (3 t), y (0) = 1

\frac{d y}{d x} = 4 x (9 - y^{2})^{\frac{1}{2}}

(10 x - 1) y^{^{'}} + 10 y = 0

What is the solution for xy^3dx+ex^2dy=0 ?
The solution for xy^3dx+ex^2dy=0 is y=sqrt(-e/(2(-ln(x)+c_{1)))},y=-sqrt(-e/(2(-ln(x)+c_{1)))}