Which differential equation can be solved by rewriting the right–hand side as a sum…

MATHEMATICS · Single correct · A Level · Mathematics · Algebra and Functions · Algebra and Functions

Problem

Which differential equation can be solved by rewriting the right–hand side as a sum of simple rational functions with distinct linear factors of

x

only? (a)

\displaystyle \frac{dy}{dx}=\frac{3x}{(x-2)^{2}}

(b)

\displaystyle \frac{dy}{dx}=\frac{\sin x}{x^{2}+1}

(c)

\displaystyle \frac{dy}{dx}=\frac{2x+3}{x(x-5)}

(d)

\displaystyle \frac{dy}{dx}=\frac{2x+1}{(x-3)(x^{2}+1)}