Artificial intelligent assistant

differential equation FP2 I am stuck on an FP2 edexcel differential equation. Q5. $(1-x^2)\frac{dy}{dx} + xy = 5x$ The answer is $y=5 + c(1-x^2)^{1/2}$ Question from fp2 edexcel book, pg 85

As Moo pointed out, it is separable:

Divide through by $x$, rearrange and integrate to get (I'm doing it all pretty much in one step since it is not considered well-mannered to treat the derivative as fractions, even though it is basically how I carry out the operation, but don't tell anyone!): $$\frac{(1-x^2)}{x}\frac{dy}{dx}=(5-y) \leftrightarrow \int \frac{1}{5-y}dy=\int \frac{x}{1-x^2}dx$$ which gives $$-\ln(5-y)+c=-\frac{1}{2}\ln(1-x^2)$$

If you solve this for $y$, you get your result.

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