# How to check work for First Order Linear Differential Equation?

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So for example, I calculated what y is from the equation. According to our book, I should take the derivative of that answer to check work. But how in the world do you take a derivative with a +C in there. The C will stay there afterwards, so there is almost no way to check it? Or did I misunderstand something?

So for example, I calculated what y is from the equation. According to our book, I should take the derivative of that answer to check work. But how in the world do you take a derivative with a +C in there. The C will stay there afterwards, so there is almost no way to check it? Or did I misunderstand something?

##### 1 Answer

The presence of

#### Explanation:

Let me explain with an example. Consider the linear first order ODE

By using standard methods you can arrive at the solution

Let us see how you can check this solution by taking the derivative. The derivative is easily seen to be

Both the solution and its derivative contain a term which has the arbitrary constant of integration

As you can easily see, the right hand side evaluates to **cancel out**!