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

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Question 12
a.

Find ∫x2cos⁡3x dx\int x^2 \cos 3x \, dx∫x2cos3xdx

[4]
b.

A spherical weather balloon's volume, VVV m3^33, changes over time ttt seconds during a specific atmospheric test. The rate of change is modeled by the differential equation

dVdt=(tcos⁡1.5t)2V2 \frac{dV}{dt} = \frac{(t \cos 1.5t)^2}{V^2} dtdV​=V2(tcos1.5t)2​

where t≥0t \ge 0t≥0. Solve this differential equation to find VVV in terms of ttt, giving your answer in the form Vn=f(t)V^n = f(t)Vn=f(t) where nnn is an integer.

[5]

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

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  3. /1.11.7 Differential equations with separable variables (A-level only)