## Exam-Style Question on Differential Equations## A mathematics exam-style question with a worked solution that can be revealed gradually |

Question id: 378. This question is similar to one that appeared on an A-Level paper. The use of a calculator is allowed.

(a) Using a suitable substitution, or otherwise, find

$$ \int \frac{x}{(3x^2 - 5)^2} dx$$(b) Solve the differential equation below giving your answer in the form \(y = f(x)\). It is given that given that y = \( \frac{1}{2} \) when x = 0.

$$ \frac{dy}{dx} = \frac{2xy^3}{(3x^2 - 5)^2}$$
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