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).
Practise AQA A Level Maths 1.11 H: Integration with exam-style questions for A Level Maths. 436 questions covering 1.11.1 Fundamental Theorem of Calculus, 1.11.2 Integrating standard functions, 1.11.3 Definite integrals and areas, 1.11.4 Integration as the limit of a sum (A-level only), 1.11.5 Integration by substitution and by parts (A-level only), 1.11.6 Integration using partial fractions (A-level only), 1.11.7 Differential equations with separable variables (A-level only), and 1.11.8 Interpreting solutions of differential equations (A-level only), matched to the AQA A Level Maths (7357) specification and written in Paper 1, Paper 2 and Paper 3 style. Every question includes a full worked solution and mark scheme, so you can see where marks are awarded rather than just whether you got the answer right.
