Lesson 1, Topic 1
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 $$y=\frac{1+C{{x}^{2}}}{x-C{{x}^{3}}}$$.