Question 11(d)

Question 11(d)

Solve the differential equation $\displaystyle \frac{dy}{dx} = xy$, given $y > 0$. Express your answer in the form $y = e^{f(x)}$

Solution

This is an example of how separation of variables can be used to solve a differential equation.

We can re-write the differential equation as

$\frac1y \frac{dy}{dx} = x$

and then use The Change of Variables Theorem to perform integration on the left-hand side.

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