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Lesson 1, Topic 5
In Progress

Pg 5 Q2 – Solving by Substitution

Show that the differential equation \(4{{x}^{2}}\frac{dy}{dx}={{\left( 2xy-1 \right)}^{2}}-5\) may be reduced to \(x\frac{du}{dx}={{u}^{2}}-1\) by means of the substitution \(u=xy\). Hence, show that the general solution is \(y=\frac{1+C{{x}^{2}}}{x-C{{x}^{3}}}\).

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