Given that y=1y = 1y=1 at x=0x = 0x=0, solve the differential equation
dydx=12xy12e3x,y≥0 \frac{\text{d}y}{\text{d}x} = \frac{12xy^{\frac{1}{2}}}{\text{e}^{3x}}, \quad y \ge 0 dxdy=e3x12xy21,y≥0giving your answer in the form y12=g(x)y^{\frac{1}{2}} = g(x)y21=g(x).
Hence find the equation of the horizontal asymptote to the curve with equation y12=g(x)y^{\frac{1}{2}} = g(x)y21=g(x).
864 exam-style questions on Edexcel A Level Maths Integration, covering 11.1 Integrating Standard Functions, 11.2 Integrating f(ax + b), 11.3 Using Trigonometric Identities, 11.4 Reverse Chain Rule, 11.5 Integration by Substitution, 11.6 Integration by Parts, 11.7 Partial Fractions, 11.8 Finding Areas, 11.9 The Trapezium Rule, 11.10 Solving Differential Equations, and 11.11 Modelling with Differential Equations. Each one has a worked solution and a mark scheme showing where the marks go.