Hi, I am doing self study and have hit a snag in the road. Can someone please clarfiy this for me. I am reading K.A. Stroud's Engineering Mathematics which so far has been great.(adsbygoogle = window.adsbygoogle || []).push({});

Consider the equation [itex]\frac{dy}{dx}[/itex] + 5y = e^{2x}

In this case, we begin multiplying both sides by e^{5x}. This gives

e^{5x}[itex]\frac{dy}{dx}[/itex] + y5e^{5x}= e^{2x}.e^{5x}= e^{7x}

We now find that the left-hand-side is the derivative of y.e^{5x}.

[itex]\frac{d}{dx}[/itex](y.e^{5x}) = e^{7x}

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Can someone please clarify how the left hand side is the derivative of y.e^{5x}.

I get that y5e^{5x}is the derivative of y.e^{5x}, but what about the first part of the left-hand-side. What happens to the e^{5x}[itex]\frac{dy}{dx}[/itex]

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# Linear equations - use of integrating factor

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