I am in the process of learning differential equations. I found an example I do not understand. I want to know how the differential equation was rewritten to make (a) the subject. I already know the solution, I only want to understand the missing step.

Where $a$ and $b$ are constants

$$\frac{dy}{dt} = ay - b$$ to $$\frac{\frac{dy}{dt}}{y - (b/a)}= a$$


closed as off-topic by user99914, Taroccoesbrocco, Namaste, Adrian Keister, mfl Aug 20 '18 at 15:21

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  • $\begingroup$ $ay - b = a(y - b/a)$ $\endgroup$ – pjs36 Dec 21 '15 at 15:21

$$\frac{dy}{dt} = ay - b=a(y-(b/a))\\\frac {\frac{dy}{dt}}{y-(b/a)}=a$$


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