1.11.7 Differential equations with separable variables (A-level only)

a.

Given that $y = 1$ at $x = 0$ , solve the differential equation

\frac{\text{d}y}{\text{d}x} = \frac{12xy^{\frac{1}{2}}}{\text{e}^{3x}}, \quad y \ge 0

giving your answer in the form $y12=g(x)y^{\frac{1}{2}} = g(x)$ .

[6]

b.

Hence find the equation of the horizontal asymptote to the curve with equation $y12=g(x)y^{\frac{1}{2}} = g(x)$ .

[3]

a.

Given that $y = 1$ at $x = 0$ , solve the differential equation

\frac{\text{d}y}{\text{d}x} = \frac{12xy^{\frac{1}{2}}}{\text{e}^{3x}}, \quad y \ge 0

giving your answer in the form $y12=g(x)y^{\frac{1}{2}} = g(x)$ .

[6]

b.

Hence find the equation of the horizontal asymptote to the curve with equation $y12=g(x)y^{\frac{1}{2}} = g(x)$ .

[3]

1.11.7 Differential equations with separable variables (A-level only) Questions