Hello,(adsbygoogle = window.adsbygoogle || []).push({});

It has been over a year since I last did calculus. And I am having trouble with my current calculus course. First here is the question:

Solve the given first-order linear equation and verify that your solution indeed satisfies the equation.

y' - 2xy = 2xe^x^2

Now I THINK I have the answer:

y = e^x^2 ( x^2 + c)

But how do I verify? I would think I simply would take the above equation and it's derivative and sub. into the equation

y' - 2xy = 2xe^x^2

If that is the case, my problem is this: When I take the derivative of

y = e^x^2 ( x^2 + c)

I have

y' = 2x * e^x^2 + 2x^3 * e^x^2 + 2x * C * e^x^2

How can I verify my answer when there is an unknown constant in my derivative? What am I missing?

Any help is appreciated - detailed if possible. Thankyou.

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# Homework Help: First Order Linear Differential Equations

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