Show that the differential equation $4x^{2}\frac{\mathrm{d}y}{\mathrm{d}x}=(2xy-1)^{2}-5$ may be r

Question

Show that the differential equation $4x^{2}\frac{\mathrm{d}y}{\mathrm{d}x}=(2xy-1)^{2}-5$ may be reduced to $x\frac{\mathrm{d}u}{\mathrm{d}x}=u^{2}-1$ by means of the substitution $u=xy$. Hence, show that the general solution is $y=\frac{1+Cx^{2}}{x-Cx^{3}}$.

Accepted Answer

$y = \frac{1 + Ax^2}{x - Ax^3}$

Differential Equations - Solving Differential Equations by Separation of Variables

Differential Equations - Solving Differential Equations by Separation of Variables

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